The 10 hours of rest need to be uninterrupted, planned, and not spent on call. Essentially, the pilots need to have 10 hours in which they are not obligated to do any work for the company at all. Note that it does not mean "10 hours of sleep", and it is up to the pilot what they do with their time off. (They can even technically fly for another 135 operator during that time, but they run the risk of being "careless and reckless" if they aren't well rested.)
NATA has an article about some of the FAA's legal interpretations (pdf) that's pretty interesting and relatively recent (2011). Their paraphrase of the FAA's varying interpretations is this:
the FAA has said that for a “rest period” to be legal it must be: 1) continuous, 2) determined prospectively (i.e. known in advance) and 3) free from all restraint from the certificate holder, including freedom from work or freedom from the present responsibility for work should the occasion arise. Being on call is specifically mentioned as not rest.
This is an interpretation that is repeated throughout a lot of articles and forum discussions. It's also often pointed out that many (most?) 135 carriers blatantly ignore these rules, as most charter operations require pilots to be on call.
You arrive at 19:00, and are done with paperwork / postflight / etc by 19:30 and leave the airport. The moment that you leave the airport is the beginning of your rest period; it will need to last 10 uninterrupted hours, which means until at least 0530 the next morning (1930 to 0530) to mean anything.
If you get a call from dispatch at 21:00 telling you about a flight that might take place in the morning and that you must be available for a call at 05:00 just in case - your rest ends at 05:00. Because your rest period ended 30 minutes early (when you were required to be available), you did not get the 10 hours of rest and can't take a flight without violating 135.267(d).
There are no explicit limits on duty time (the exception being 135.267(c) involving a "regularly assigned duty period of no more than 14 hours" which doesn't apply to most 135 operators). The limit is on planned flying conducted under 135.
As long as you plan on parking the airplane when you can show 10 hours of rest in the previous 24 hours (which is why some people incorrectly assume that you are limited to 14 hours of duty: 24 - 10 = 14!), you can be kept on duty afterwards. You can even fly under Part 91 for the company. You can clean the airplane, or do office work. While none of that is rest and it is still duty, it is legal unless you get in the airplane to fly under Part 135 without getting the required rest.