How does Signal Analyzer measure EVM
Does it calculate the EVM of each equalized received symbol with a closest ideal symbol on the constellation and then average it out to give final EVM value?

You very rarely test EVM on a low-SNR signal that's not according to any standard, especially because if that signal doesn't adhere to any standard, there would be very little for your signal analyzer to do equalization with.
If you buy a signal analyzer, you can often buy extensions that allow you to estimate properties of some specific communication / broadcasting standards (LTE, DVB-T, VDSL,…). Such standards have channel coding, with which you can (most of the time) recover incorrectly received symbols, and then actually calculate the error between reception and actually received symbol.
In other words, to know what your signal analyzer does in your current situation, you'll have to read its documentation.