New Landlord, Tenant ignored 30 day notice to quit

[Account Closed]

I bought my first two-family last month. I'm supposed to be an owner-occupant however the tenants were given no notice by the previous owner and have not complied with the 30-day notice to quit I gave them at the end of April. They're not combative but nicely said they couldn't uproot their family on that short of notice. They since decided they wanted to buy a house and have claimed to me that they've had an offer accepted and could begin moving out as soon as July 3rd (a Sunday?) -- They are being vague beyond that. I already gave them notice that the rent will be increasing significantly to market rates starting in July. What else should I be doing? Should I be filing with the court  just to keep the timeline moving even though they said they'll move out next month?