100A sub #4 wire??
I also agree #3 is required for the sub panel feeder. But nap makes a good point about article 310.15. Looking at 310.15 below its says 3 wire. Feeders today, unless in metal conduit, must be four wire. Services can be 3 wire regardless of the conduit. So I am of the opinion that any panel after the service panel uses artical 310.16 not 310.15.
Table 310.15(B)(6) Conductor Types and Sizes for
120/240-Volt, 3-Wire, Single-Phase Dwelling Services and
Feeders. Conductor Types RHH, RHW, RHW-2, THHN,
THHW, THW, THW-2, THWN, THWN-2, XHHW,
XHHW-2, SE, USE, USE-2
Conductor (AWG or kcmil
OP. Do not fear. Just go and get a 90 amp breaker and install it. I would not allow the other guy back into my house. If he bought the same wire you already had, he either knows something we don't or he is a hack.