A concise way to describe the situation is that during sustained inverted flight, if the aircraft is banked away from wings-level inverted, the flight path will curve toward the wingtip that is closer to the earth. This is a bit odd because the flight path ends up curving AWAY from the direction of the initial roll, i.e. away from the direction that the pilot moved his control stick or twisted his control yoke to start the roll away from wings-level inverted. During inverted flight, if we bank aircraft toward the left, from our perspective sitting in the aircraft, the nose will start tracking around the horizon toward the right-- toward the earthward wingtip.
An interesting consequence of this is that during sustained inverted flight, to neutralize adverse yaw and keep the nose lined up with the flight path as we roll (change the bank angle), we have to apply rudder OPPOSITE to the direction that we are moving the control stick or twisting the control yoke.
However, lest we lead the reader astray, let's note that the adverse yaw issue in practice isn't so severe as to prevent the aircraft's heading from swinging in the direction of the earthward wingtip, perhaps after just a slight bit of hesitation. In other words as we fly wings-level inverted and we move the control stick to our left, we might see the nose swing a few degrees to our left for just an second or two but then we'll see it begin to track around the horizon to our right, toward the earthward wingtip, as the flight path curves toward the earthward wingtip, even if the nose remains yawed slightly to the left of the actual direction of the flight path at any given instant, until such time as we end the rolling motion and stabilize at a constant bank angle, at which point the adverse yaw effect largely vanishes and the nose tends to become (almost) fully aligned with the actual direction of the flight path at any given instant as the turn continues. The whole adverse yaw issue is much more likely to be noticeable in a long-winged aircraft like an aerobatic sailplane, than in something like a Pitts Special. (In the Pitts the required rudder inputs will probably have more to do with engine torque and P-factor than with aerodynamic adverse yaw!)
And yes, this is all a result of the fact that we've put the wing at a negative-lift angle-of-attack, usually by pushing the control stick or yoke forward. If we unload the wing to the zero-lift angle-of-attack (at which point we'll go weightless in the cockpit), adverse yaw vanishes and we don't need to coordinate our roll inputs with rudder inputs. We also no longer see the flight path curve toward the earthward wingtip. If the wing is at a positive-lift angle-of-attack during inverted flight (e.g. at the top of a positively-loaded barrel roll), to keep the nose lined up with the flight path, we'll apply rudder in the same direction as we're applying ailerons. We'll also see the flight path curve toward the skyward wingtip rather than the earthward wingtip.
The easiest way to quickly understand all this is to "fly" through the maneuver with a little hand-held model of an airplane, thinking about which way the pilot is moving the control stick, which direction the bank angle is changing, and which way the wing's lift vector is pointing. Whichever direction the wing's lift vector is pointing, is the direction that the flight path will tend to curve, causing the nose to tend to track around the horizon in that direction. And as far as adverse yaw goes, and the direction of required rudder inputs, keep in mind that as the aircraft rolls, the wing that is moving (rising or falling) AWAY from the direction that the lift vector is pointing tends to "drag back"-- actually this has to do with "twisted lift" (see https://www.av8n.com/how/htm/yaw.html#sec-adverse-yaw ) as much as actual drag-- requiring a rudder input toward the other wingtip. Again, fly it through with a hand-held model and it will become clear.
In relation to adverse yaw and required rudder inputs, this answer could reference "keeping the ball centered", but note that during negatively-loaded flight, the tube of a conventional slip-skid ball curves the wrong way, so during sustained inverted flight, the ball will tend to end up "stuck" in one corner most of the time. Some aerobatic planes sport an upside-down slip-skid ball on the panel in addition to the normal one. If the G-load is near zero, the ball will become hyper-sensitive (regardless of which way the tube is mounted) -- the least bit of sideforce will send it to the far corner or the tube. A glider's "yaw string" continues to work just fine even when the G-load is zero or negative.
By the way, with a radio-controlled model aircraft, during negatively-loaded (sustained inverted) flight with the aircraft flying away from the operator who is standing on the ground, if the plane is banked away from wings-level inverted, the flight path will curve TOWARD the direction that the operator moved the control stick to initiate change in bank angle. Again, this is toward the earthward wingtip.
This answer is probably more easily understood if the reader keeps in mind that the direction of the wing's lift vector, and the direction of the G-load, are essentially the same thing (or we could say mirror images of each other.) If the wing's lift vector points toward the pilot's head, the G-load is positive, and if the wing's lift vector points toward the pilot's feet, the G-load is negative. If the wing is at the zero-lift angle-of-attack so that there is no lift vector, then the G-load is zero, at least in the up-and-down direction in the pilot's reference frame.