All trainers have different opinions. Some gyms throw people in at the deep end and see if they sink or swim. It does sound that this particular gym is quite tough in that regards. Truth is there is no real right or wrong way as gyms with very different philosophies end up having very similar succes.

Personally I'd prefer a gym where they weren't quite as tough. With regards to sparring, most gyms are eager to get you in there sooner rather than later, but usually against a more experienced fighter (so you can learn from him/her) and usually held on a tight leash. You learn more in your first round of sparring than your first month on the mitts, where you really have to start being conscious of distance and start to appreciate how much work really needs to be done to climb in this toughest of sports.