Is this project for fun or a school project? At least take the effort and practice good wire splicing techniques. Does the wire you used look anything like the wire your home is wired with? You have the common sense to use an isolation transformer that's good, but you seem to have very little 110VAC electrical experience. Take a course, they teach this stuff almost everywhere even if it's just to get the basics. Your local library will also have plenty of books on home wiring, worth a look at the very least.
From wikipedia on Solderless Breadboards.
As for the "Electronics for You" burglar alarm, you'd think the publishers would have the savvy to test their articles. The OP should have written them about it.
As for the smoke... give it a chance, put enough current / voltage through those breadboards and they will arc, probably already are. Over time the contacts will pit and the electricity will start looking for a shorter path as the resistance increases. Puddles o fun.
If this IS a school project STOP it's a bad one
If this isn't and you need a light dimmer, you're in BC you can get em anywhere for a few dollars.
If you're trying to learn electricity then learn the basics first.
If you're trying to burn your house down then proceed, don't expect your insurance company to cover it though. Not really CSA or UL approved
PS never trust any electronic projects on the Aaron cake site. It's a bit of a joke round here.
https://www.aaroncake.net/circuits/dimmer.asp