So, I have noticed what you are seeing with most of my LCR meters and where it seems to come from is the handling of the component. If I pick up the component by the body and insert it into a fixture, then I see exactly what you see. Resistors going up in value, capacitors going down, for a couple of minutes, then finally stabilizing If I pick up the component by the leads (or tweezers for SMD), not heating the body of the component with my fingers, I get a stable reading right away.
I just measured a 50uf cap. When I picked it up by the leads, it read 64.400 uF right away and stayed there (varying +/- 0.001). Taking it out by holding the body, keeping between my fingers for 10 seconds, then re-inserting it, it initially measured 64.559 uF then over 5 minutes returned to 64.400 uF.
If you need a quick reading, do not hold your components by their body before inserting them. Otherwise, if this is not possible, give them 5-10 minutes in the fixture for the temperature to stabilise before recording the reading.