In case of air to air refueling, the 'receiver' (the aircraft being refueled) should be careful about not getting into the wake of the tanker, which is usually much larger and heavy. For example, the NATO air-to-air refueling manual, ATP-56 specifically states:
The area of extreme turbulence directly behind and slightly to the right of the tanker should be avoided. Blade stall and uncontrolled settling may be encountered if this area is entered.
The receiving plane is usually flown below the wake turbulence of the tanker, in both the hose & drogue and flying boom methods. Usually, the receiver is directly behind and around 10' below the tanker. For example, see How do aircraft refueling in-air deal with wake turbulence?
In addition to turbulence, in case of close formation flying, there are other things to contend with, as explained in Advances in air to air refuelling:
In addition to the trailing air vortices the receiving aircraft must contend with downwash of airﬂow from the tanker. The affected local airﬂow typically exhibits a nose-down pitching moment on the receiver which, in turn, affects its speed and approach rate.
Not only the receiver, the tanker should also be careful about flow disturbances.
... mostly between large transport aircraft, the lead aircraft experiences a change in its airﬂow caused by the bow wave, or upwash, from the receiver. This increases the angle of attack around the tanker's tail which also results in a pitch-down motion.
Under-running the tanker is particularly dangerous since the downwash effect will dissipate, resulting in the receiver pitching up. At the same time a tanker on altitude hold may instigate a nose-down pitch due to a perceived climb due to the decrease in pressure in the surrounding air, potentially leading to collision.
The figure below shows some regions where disturbances would be encountered aft of a tanker.
Typical spanwise airﬂow disturbances from a trailing tanker wake.; image from Advances in air to air refuelling by Peter. R. Thomas et. al.
In addition, the trailing aircraft should also be careful about the jet exhaust.