How long have you been on the mini pill?
Are your periods usually quite regular?
Have you not had irregular bleeding before on the mini pill? Thank you.
Pregnancy is unlikely to be the cause of your bleeding. It's much more likely that the bleeding is just a side effect of the mini pill, which is very common.
It is important to take the mini pill every day, as missing a day can possibly result in pregnancy. But still not very likely, and irregular bleeding on the mini pill is very common, even in someone who hasn't had such bleeding before.
When there is going to be irregular bleeding from any cause, it often comes after having sex, for some reason.
Pregnancy is also unlikely because it would be quite unusual to get pregnant having sex day 5 or 6 of your cycle. Plus you then had a normal period June 6, although an early one.
So I think that pregnancy is quite unlikely. If you do develop any symptoms, I'd do a pregnancy test, just to be sure. Otherwise I'd keep taking the mini pill daily. Best wisehs.