What's the phase relation between the sine wave and the sync output from a function generator?
It's also worth noting that when I generate a square wave, it overlaps with the trigger pulse exactly.

This may be a clue. It would be logical to use the same squarewave signal for both.
The better question might be, &quot;How is the sinewave generated from the square?&quot; If this is done by look-up table, for example, then the trigger point could be any point on the waveform and a non zero-crossing choice would be strange.
I had a look for a random signal generator manual and foun the TTi TGA1240 Series 40 MHz Arbitrary Waveform Generator which states:

Waveform sync
A sync marker phase coincident with the MAIN OUT waveform of that channel. For standard waveforms, (sine, cosine, haversines, square, triangle, sinx/x and ramp), the sync marker is a squarewave with a 1:1 duty cycle with the rising edge at the 0° phase point and the falling edge at the 180° phase point.

At least this one works as you expect.