I was told in the beginning that they would contact me for the SSDI reviews and to wait until contacted; you can confirm this though with your local social security office or online at their website in case this has changed. That said, I was told in the beginning like you that I would be contacted in 18 mos but it turned out to be 26 mos later that I got my first review, and then, in a total of 14 years now, I have had 2 reviews.
I did not have improvement in my status during this time, however, which might be what the difference is as there are set periods of time established for the reviews whether you are deemed temporarily or permanently disabled (see online or with your local ofc, I think it is 3 years for temporary disability and 7 years for permanent). This will be changing for me now that my status has changed and am attempting to return to work; we'll see what happens.
I have always been contacted by letter with a form to complete but know of others that have gotten a notice in the mail to set up a phone interview, that asks the same questions as the written form. It is a fairly simple and straight forward process, nothing arduous like the application process.
If concerned, I would verify the procedure as whether to wait for SS to contact you or you to contact SS about when you have a review. I have stuck by the original instructions of waiting for them to contact me but this may have changed; I should find out myself too.
Hoping all goes well with the private disability insurance meanwhile.