Irregardless of if they are legitimate companies, you should not be getting offers without you initiating them. To join a mystery shopping company you should go to one of the companies listed on the bottom home page of this site and join them. An unsolicited offer is probably a scam.
Both Jancyn and Ellis have reported that their names are being used by scammers. Neither one cold contacts individuals to offer shops. Before they will contact you with potential assignments, you would need to have logged in to their websites, registered, and provided your Social Security number.
Both are great companies to shop for; however, must warn you the reports for Apartment shops for Ellis will drive you to pull your hair out (repetitive and very long). I shop for Jancyn monthly - quick and easy sizing audits that can be done and reported in under an hour.
I want to add that I sometimes get referrals to other companies from schedulers that have gotten my name from a different source...perhaps I did a shop for them or another scheduler they know. If you get a referral like this it is probably legitimate but you should still go through the website of the company they are referring you to. Many times it is a scheduler I have worked for. Contact the scheduler you know to make sure they really did refer you.
I, too, have received offers from companies I am not signed up with. Usually the e-mail is prefaced with "Scheduler XXXX from XXXXX MSC referred me to you as a possible shopper for XXXX", thus immediately introducing themselves and how they got my contact info.
Some of the most remunerative shops I have ever received have begun in just that way.
While both EPMS (Ellis) and Jancyn are very legitimate companies, neither goes by the exact name you have quoted above. If that is how your contact/s named them, this is almost certainly a scam.
Use the links in the "Official List of Mystery Shopping Companies" linked below to find the real companies. Both are great.
Another bright red flag: Were you sent a check (a large one, perhaps), for work not yet performed? We you asked to use that money to purchase gift cards? Were you asked, for Ellis, to do anything besides visit apartments?
Hard work builds character and homework is good for your soul.