Yes indeed, there absolutely are a standard set of handsigns for indicating air pressure. As a matter of fact, there are quite a few of them!
Seriously, I think every place I've been has had their own special variant of the pressure handsigns. I always screw them, up on the first few dives with any operation that is new to me. The standard one I like best is simply "just show me your SPG." I know that means that if there is a DM, he has to swim around to each diver but that's why he gets paid the big bucks.
Regarding the OP, I will embellish on what Soloist said a few pages back. You said this guy had been away from diving for a while. Well, he might have been a real old-schooler who'd never learned the new-fangled NDL concept. Back in the day when we had to fashion our own goggles out of octopus eyes and carve our own air cylinders out of out mud using sharpened sticks, the concept of adhering to NDL limits was not really taught as an important safety consideration. You knew that you were unlikely to breach the deco limit diving steel standard 72 cu ft tanks but "nonstop diving" per se for it's own sake was simply not really a thing. For your basic c-card, you learned the from the Navy deco and repetitive dive tables and you were taught gas planning. You planned your dive with tables before diving and if you had doubles and might go into deco, you curtailed your bottom time to allow extra gas for that deco. You could hang extra bottles but only professionals/military did any kind of mixed gas diving or O2 deco.
If this guy was trained in the way back he may never have heard the acronym "NDL" used in this context before even though he may have had a reasonable basic education in decompression in general. As for not knowing about the computer... back in the dim ages, we all used tables and memorized many of the values though simple repetitive use. He may have been simply going on memory and wearing the computer because he had to have one. The no decompression limit for a 35 ft dive was 310 minutes in the Navy table so a 45 minute dive to 35 ft with a 45 minute SI... hardly worth the bother to even count it as a dive. The Navy table limit for the next 85 ft dive (90 fy limit) was somewhere around 1/2 hour... Not to worry. Just limit your bottom time. (Exceeds modern/computer limits and locks up the rec computer? Yes.)