Pest Control isn't the owners responsibility under the Act, however if it states it in your lease, than it is the owners responsibility. Pest Control can help with the removal of spiders, however ants are very hard to get rid of. Many pest controllers won't even treat for removal of ants as it does not work.
ETA: I forgot to say that definitely send out a NTR. As it's in the lease, they've kind of put their foot in it, and have to get it done now.