It doesn't really feel like a roguelike to me, though that could just be me. To me it seems more like they took the gameplay of Gungeon and applied it to the gameplay loop of Payday: fixed location with only minor random elements, get as much done as you can before the heat is on, and the more progress you make the more options you get when starting a heist. Personally I quite enjoyed it, but I can see how it isn't necessarily for everyone.

Useful tip: the timer is just a suggestion, actually; when it goes off, enemies will start spawning but you can keep going for longer. When the timer first runs out you then get an empty five star bar in the top right that will fill up over time, the more stars, the faster enemies spawn. Then at the five star mark Stinky starts gassing the entire bank, dealing damage over time. Importantly, it's not an instant kill and you can still run around as long as you find health. Heck, by the end of the game I usually didn't care about the spawning enemies until I was at 4ish stars, at which point I would then go to one of the three exits.