Circuit tester trips new GFCI
As well it should.

Normally, loads are connected between hot and neutral.  Appliances are not supposed to connect hot or neutral to ground; ground is only a shield. 

The GFCI compares current on the hot and neutral wires.  They should be the same.  If they are not, current has found another route, possibly through the grounding system (which isn't supposed to happen) and potentially through some poor human.  

Circuit testers are trying to test whether ground is connected... cheaply.  They mis-use "hot" as a power source, by connecting a light bulb between hot and ground.  If ground is connected correctly, this will light.   

In other words, it intentionally creates a hot-ground fault (by sticking a light bulb there).  This is exactly the condition GFCIs are designed to detect.

I'm not talking about any ground-fault-test the tester may also have.  

So why do testers often work?  With a perfect GFCI, they wouldn't work.   I suspect it is because GFCI's have detection thresholds above zero, and that is often enough for these testers to "get away with it".  I even think there may be a tacit agreement among manufacturers for this, but obviously, lower sensitivity impinges safety.  Remember a shock which only stuns you can kill you with secondary effects like falling or drowning.

So either your GFCI is pretty good, or your tester is pretty bad.