I can't tell you how it works "exactly", but I'll give you a general how it does.
The push rod on the tensioner contacts the tensioning rail, pushing the chain toward center, in effect removing any slack. When the engine is run, the oil, which is now under pressure, enters the tensioner at pressure, further tightening the chain. There should be a check valve inside the tensioner which will keep the push rod extended even when the engine isn't being run, so the chain is properly tensioned at the next start-up. As the tensioner gets old, the check valve leaks down, and that main spring you had to work so hard to compress (to install the new tensioner) gets weak. Lack of retained oil pressure and that weak spring cause chain rattle at start-up, continued chain rattle can cause a chain failure resulting in several thousand dollars of damage.
Again, roll it over through two complete revolutions before you do anything (I'm a little OCD when it comes to hand cranking, I'll go four complete revs - on the 560 I did six, only to learn it takes six and half to make the chain complete one revolution). If the timing has somehow gotten off, you will eat valves on your first attempt to start.
'73 280SEL 4.5 (9/72)- RIP
Only 8,173 units built from 5/71 thru 11/72
'02 CLK320 Cabriolet - wifey's mid-life crisis
2012 VW Jetta Sportwagon TDI...at least its a diesel
Non illegitemae carborundum.