The stock Tandy 3.5" drives in those machines receive power over lines that are normally disconnected or connected to ground in standard floppy drives; the first five or six normally-ground pins are +5v , the last three are +12. Obviously connecting +12 to ground is a bad thing, so you may have destroyed the floppy drive you put into the machine by hooking it up like that. There are also other issues; a standard PC floppy drive is jumpered as device #2 and is set up to accommodate the monkeyshines with the select and motor signals that IBM did on the IBM PC, while Tandy used standard Shugart conventions and therefore wants drive A to be jumpered as device #1, but the power thing is the main killer.
Here's a thread I made about the quick-and-dirty method I came up with to defang the power pins on the Tandy connector using a simple stacking header. You still need to deal with the jumpering issue (seems like most more modern 3.5" floppies don't have the jumpers to be configured for anything but a PC with a twisted cable) but you can use this technique to at least solve the power problem.