So maybe the bit of underexposure isn't related to the development time/temp at all -- just means this film needs to be exposed at 800. (I exposed at 1250.) Thanks.
Essentially, yes. But there are a lot of moving parts.
1250 is a very reasonable exposure index for D3200. But I recommend backing up a little and approaching this more fundamentally.
You, your methods, and your gear are the biggest variables here. The great thing about a "lab" is they tend to be consistent—they are a laboratory—as long as you have good communication with them. The chemistry is relatively consistent. The film stock is consistent.
The important questions is: How do you want your negatives to look in order to get the results you want, and what methodology gets you there?
The way I handle a light meter may be different than you. Your camera may be better calibrated than mine. The shutter speeds may be more accurate. Or, I might shoot in more variable lighting which favors erring on the overexposed side. Or, you might prefer the esthetic of a thinner and more contrasty negative, and maybe you shoot in flatter lighting scenarios. Who knows.
I said I shoot D3200 at EI 800. That's just what works for me. But I don't think of 800 as a scientific or technically ideal "normal" speed. It's the EI that gives me negatives I like for a lot of shooting scenarios. It's also possible that when I shoot at 800 my negatives turn out very similar to another person who shoots at 1000, 1250, or 640. The lab also learned what to expect from my negatives, back when I worked with the same lab frequently. So, if I came in and was uncertain about a roll and said "I think we need to push this roll two stops" they already had an idea of what that meant and how to proceed.
I also want to mention is that when you're shooting high speed film, it's often a very different situation then when shooting slower films. Darker scenes can have more complex lighting. You may be shooting wide open when using D3200. But maybe you shoot at f/8 more often with a 400 speed film. Wide open, you're more likely to have modest underexposure due to falloff and slightly BS nominal, factory aperture (an "f/2.8" lens that's closer to f/3.5 when wide open).
This is getting a little bit rambling, and I don't feel like editing much. So let me get back on point:
I recommend shooting test rolls. Is your light meter accurate (EV 15 in open sun?). Is your shutter accurate? Are your lenses stopping down smoothly? OK, let's assume yes to all of those points.
To find your "normal" for a film using 120 film: Select a scene with whatever you consider to be "good" and with steady and even light. Shoot at a middle aperture, not wide open. Heavily bracket the exposures. If you want to do this with a 3200 speed film, I would shoot all the way from EI 200 up to 6400 in 1/2 stop imcrements. Take notes, and bring those notes with you to the lab. Tell the lab what you're doing. Ask them to develop the film without a push. Ask them what speed they think that is. Look at the resulting negatives and decide which exposure got you the best results. This will establish what your normal
exposure should be. It doesn't matter what "speed" the lab calls it. Your exposure determines shadow detail and midtone placement. Whichever negative looks and works best for your preferences is YOUR film speed for this film.
Once you determine which exposure looks best, you can start thinking about overall contrast. Negatives too flat? Ask the lab for a +1 push process. Don't say "develop for 1600." Tell them you exposed normally and want a one stop push.
You can repeat the test for push processing if you want. Expose another roll in a similar scene but this time expose for EI 800 through 25000 in half stop incriments. Tell the lab what you are doing. This time, ask for +2 stops push processing.
Once you get these test rolls sorted out, consider annotating them with a sharpie directly on the negatives, or taping your notes to the negative sleeve for reference years from now. I have some of these test rolls from 25 years ago. They're still interesting to reference.
I swear it will be worth the trouble.