so a chunk of the rubber bead came away from the cords around the rim seal?
that sounds like old dried up tires to me. i bet the tire tech tore it when he was running the duckhead around the rim to instal em. you will most likely notice cracks quite quickly and they may even throw belts before you even get 10k on them. they may also completely shed the tread patch and/or explode.
i used to see people with old tires from salvage-yards come to me wanting them mounted because they couldn't afford the cheapest $40 tire we sold... i could lube the beads as much as possible and still tear the damn things trying to run the beads around the rim on the tire machine... sometimes most of the entire bead would come away and it would never seal. and needless to say, salvage yards don't warranty used tires, so these poor sobs usually ended up spending another $20 on a second old dried up pile of crap when they could have just got a brand new (albeit cheep) tire from me in the first place and i could have mounted it with no problem.
old tires dry up like a prune...
its why i recommend you should NEVER get your old fullsize spare down from your old 90's beater pickup and run it down the road. replace it 'new' or not every 10 or so years. under a cover, inside the cab, doesn't matter where its been stored, it will be hard and inflexible as a rock. same thing happens to warehoused tires, they really don't even have to be mounted like others have said already.
used to see that a lot as well... people coming too me wanting their fullsize spare transferred to their alloy after a blowout. usually ended up destroying the bead trying to remove it from the rim. i outright refused a lot, especially if the tires they had were bald as hell. nothing chews up a transaxle or diff like putting a good tire on the same axle with a bald tire
love tires, most important part of the car imho. and the most neglected >.>
just ask yourself, where are you going without em?