Welcome to the real world of employment!
No - they SHOULD not call you back when they said they would. It would be nice if they did, but its their job, their circumstance & the ball is completely in their court.
Now...to give you some perspective on how technician employment works.....you apply & if your application looks at all good, you'll get an interview. After the interview, they'll check your references - both "officially" and "unofficially". Officially means they call your past employers & the only data they'll get is dates of employment & official disciplinary actions. That will check out if you lied on your application. They'll also look in their past records to see if you've been employed anywhere else in their system.
Now...the "unofficial" reference is done by having the dms or rpms - whatever the company calls the person in charge - he or she will call his/her friend in your past employment situation if its in pharmacy & chat about new products, wholesaler situations, reimbursement issues & oh - you'll come up as well. Its always done obliquely - nothing is ever documented.
Now it comes to the timing. You had your interview the Friday before the first real holiday of the summer. Folks took off from Sat-Wed, or Mon-Wed, or Wed-this Fri...whatever. When a holiday falls mid-week - nothing administrative of any significance goes on.
So - what do or can you do? Nothing - you just wait. How long? I'd give them until a week from this Friday - about July 13. That gives everyone a full business week to do what they need to do to check you out. It also gives the dm a chance to check with pharmacists in the area to see what their needs are. If you have no experience - you'll need to have some techs around who can spend time teaching you. If you have experience, you'll need to be in a place that can take the hours you're looking for.
My advice - wait another week. Then send a nice polite phone call just checking on the status of your application & to please contact you if there is anything further they need.
Good luck!