I would say generally tenants' responsibility, but I would also go to/call the real estate to let them know, especially what neighbours have said, re previous infestations. I would also do what I could to affordably get rid of them myself.

That said, we have them in our new rental, and (just having a little vent here, don't mind me!) due to lack of shelving and storage, we have lots of boxes stacked up in the house and carport, and I suspect there could be a nest in the dining room . I put out a trap last night with peanut butter, and the little blighters just licked all the peanut butter off and the trap didn't go off! And it's those awful traps that will nearly take your finger off. Waaa. Have reset both traps today, smooshing the peanut butter under the little spike thing. :fingerscrossed: