You could've gotten old, bad cells, but my chart from Maxell says the 386 is silver oxide, and the L1142 would be alkaline. I can't say myself, but some devices and testers may be more chemistry dependent than others (voltage, current draw, internal resistance, etc).
Usually, I keep several spare cells on hand, and I'll certainly try an equivalent size cell if I don't have the exact replacement, and usually it works fine.
Maxell chart:
http://biz.maxell.com/en/primary_bat...erence_16e.pdf