Hey, your employer is NOT the job site where you worked. Forget about saying anything to them. They don't care. You were an employee of Tempservices-whatever-they-are, on assignment at wherever they chose to put you. Your wages and your unemployment insurance taxes on wages were paid in by the temp service and they are your separating employer, the ones who will be contacted by the unemployment system. It is not necessary for you to contact them or anyone else when you are separated. I know it was hard for you to remember that during the lengthy time you were there on that site, and to feel that the jobsite employer is not the ones that should be separating you. But they're not.
When you are released from your assignment, after that last day of working there, you'll need to talk with the temp service, make it known to them that you are available for further job assignments. If you've not been actively in contact with them, do so at once. That will be the big issue with your getting unemployment benefits. Most temp services have requirements in place that you must check with them on a regular basis to make sure you are still available for other assignments they may have for you, and should you refuse such an assignment while drawing unemployment insurance, they'd report you and there'd be a big issue with your eligibilty. Temp services are very familiar with this process.
You don't need to be an expert before you sign up for unemployment benefits. It costs nothing to sign up, there is no downside to it, you either are or are not going to qualify. And it is not based on how much you need it, or your being able to argue for it brilliantly. But they will quickly tell you, when you begin to file, who your separating employer is when you work as a temp.
The system will have your wage records on file, they'll pull up your wages for the past 18 months and determine if you have worked enough to set up a claim. Then they'll do a determination based on the reason you are no longer working for your previous employer, which is, remember, not the job site, but the temporary service.
They'll take your side of the story (assignment ended) and they'll confirm this by contacting the temp service, and you'll get a decision on your eligibility for benefits. Meantime you'll be filing for weekly certifications. It will take two or three weeks to get this all set up in the best of circumstances.
No the employer is not the one who says whether you get benefits. And it is not something you could set up by talking to them beforehand anyhow. But in the case where your employer is a temporary service, they will be able to , and definitely want to keep their labor pool in thrall, so to speak, so if you are receiving benefits, with the service as the separating employer, you will be keeping in steady contact with them and always must be able and available for that next assignment.
