The "till" is quite informal (and sounds a little dated). You could say: "They put me on the (cash) registers." or "They have me working (at) the (cash) registers."

"They've put me on the till" if there's one till, or "They've put me on the tills" if there are several. "On" is better than "at", because being "on the till" is a job within the store "At the till" is more of a location : for example, the customers would be told to pay at the till.

I would say, "They put me on the (cash) register."

Theyve put me on the till's