Ok, there is a common misconception about 3 ways.
How are checking vor voltage at fixture hook up?
If you are using a no contact detector it will show power no matter which position switches are in.
Your explanation appears to be correctly installed.
Hot comes to first 3 way to common screw
Then travelers from 14/3 wire goes from 1st 3 way to traveler screws on 2nd 3 way.
At 2nd 3 way black from another 14/2 wire goes from common screw to the fixture.
If this is how you ran it, try hooking a light up to test. I think you'll be pleasantly surprised