A319 Captain reported the Tug driver interrupted the pushback to secure the DG cargo. The Captain further stated that Dispatch took 30 minutes to inform the flight crew that the DG cargo was exempted from providing a NOTOC during pre-flight.

Narrative

After we completed the Prefight and Before Pushback checklists; ramp advised me they were ready for brake release and pushback. I released the Parking Brake and immediately after I released the Parking Brake; the ramp lead told me they needed the brakes set again because they had to put 15 more bags on and they were going to put them around the package with Lithium-Ion Batteries which immediately got my attention as I had no notification of any DG onboard but had released the Parking Brake. I was not happy that the ramp purposely led me to believe that we were ready to push but knew they needed to put more bags on but couldn't get an on-time departure without playing games to circumvent our procedures. I complied with resetting the brakes. Eventually this practice is going to lead to someone getting hurt. The other issue was what about the lithium-ion batteries. I immediately contacted load planning inquiring about the possible DG and no notification. I also contacted ZZZ Ops and my Dispatcher. It took about 30 minutes to get an answer that I had been loaded with an exempted 92 lbs. package with lithium-ion batteries in it. Nobody could get a hold of the dangerous goods people to know what the package was for at least 30 minutes. When a Ramp Person tells me I am carrying something that is a known dangerous good in the cargo hold where it generally isn't allowed to be carried; and I can't get any other information; there is no way I'm going to pushback until I get more information. After departure; I was eventually advised by Ops that it was parts by a known shipper for Company. I truly don't know how we get authorization to ship things like this without notification to the pilots. In the event of a fire I would not be able to notify firefighters of location nor type of DG. That is clearly a hazard in my book.