When RSU vests, it is no longer an RSU. Not sure why you would call it “dividend-equivalent” as they are regular dividends at that point (unless your broker lends them out in which case you might get substitute payments in lieu.)
I'm just using the terms that show up on my etrade plan confirmations. In lieu of actual dividends, the terms of the grant say the company will issue RSU dividend equivalents, commensurate with what the dividend would have been had it been purchased on the grant date (or something similar, I don't have that paperwork at hand).
I suppose that might be some special amendment in your specific RSU plan electing to pay some cash on top, not inherent to the nature of an RSU, which is certainly not a stock (i.e. on the corporate financial reports that payment would not be showing up as a dividend).
