Is it normal to have zits on the butt? Did I get them from partner?

No. This is probably skin infection from staph. This is not necessarily from your partner. Some people have a local poor immune system which allows a normal bacteria to cause an infection.
Butt folliculitis. The causes of folliculitis on the buttocks vary but some common causes include irritation from non-fragrance free detergents or fabric softeners, stress, hormonal changes (not just women, men can have hormone fluctuations too), or perspiring under tight-fitting clothing. When you perspire with snug clothing on, perspiration from your sweat glands, your natural body oils and bacteria can clog pores.