Tenants want to push back move-in Date

[John Frank]

So I like to be proactive in tenants moving out and new tenants moving in so I keep my vacancy rates low.  I have know since February that my tenant was planning to move out at the end of her lease which ends on May 31, 2017. After about a month and a half of screening prospective new tenants, my wife and I fell that we found new tenants for our property.  We signed the lease for a 12 month duration, from June 1, 2017 to May 31, 2018, in April with the expected move-in date of June 1st.  I did explain to the new tenants that if there was no problem with the previous tenants move-out then they should be good for June 1st but there move-in date may change  no more than a couple days if there are any issues that I need to address before their move in (Previous tenant was only in property for 6mo's after my initial rehab so I didn't feel that I would have anything major to fix).  We have set a final walkthrough for May 27th and in keeping in contact with my current tenant, I know that she has been almost completely moved out since the begining of May.  In knowing this I am sure that there shouldn't be any issues with the new tenants move-in date which I had informed them of this at the beginning of May.   So I just get a message today from the new tenants that they want to push there move-in date back to June 11th.  I am not sure how to answer this as I don't want to start our relationship off on the wrong foot.  I feel that If I give them a break, they are going to think I am a pushover and it is going to start the beginning of constant requests to bend the rules.  Is there a way that I don't have to be a complete @#s about this and give them a break or should I hold to the rules to set the tone?  Please help?