Hi all!
So, in order to not to leave the Fermat's post, the solution has been found. It was found, that different HPE devices have, let's say, quite a different implemetation of EVI. I have the 7900 switches in my case with FX modules. It is important though, because EVI has problems with other module types - I have found the doc describing it somewhere on HPE site, but now can't.
So, the solution to set up EVI (if you also need routing/VRRP on the same switch) on the 7900 switches is to create a separate MDC for routing and use EVI on the default (Admin) MDC. So you'll get two separate logical devices, one will perform EVI and the other will perform routing and so on. You can find some info here:
http://h20195.www2.hp.com/V2/getpdf.aspx/4AA5-6480ENW.pdf
Another awful thing was the EVI docs for 7900 switches. It really explains nothing - so it is written in a way like "if you want to configure EVI enter this commands". And there are some unobvious things in EVI configuration - and I've found explanation for them in 6602 Routers docs, so I would recommend using it.
The most unobvious thing is enabling evi on the physical interface. In 7900 doc it is stated that you must enable it on the physical interface from which the EVI tunnel is built. Hovewer, in the real world, if you connect to different EVI sites (especially the ones, facing each other through L2 as I have) you must not enable it. Evi enable command on physical interface should be configured when you configure link between two evi devices on the same site. So if you enable it on the different sites facing each other through L1/L2 you'll get the site-id conflict and still the doc for 7900 switch would say that you have to enable it. Ridiculous.
The same thing is regarding "evi designated-vlan" command. It is not even present in the doc for 7900! However, it is in 6602 doc. So, what it does? Practically, the same, that "evi enable" - it designates a vlan, which should be used by two same-site devices to communicate the evi information. So, again if you have two L2-facing sites, you might get wrong and get a site-id conflict again. What is the most funny thing, that this command does have the default value. So, the default value for evi designated vlan is "1". And think what? If you have (you should almost surely have) trunk or hybrid interface between your two sites (if you have L2, as I have already mentioned) and forget or even contiously leave vlan 1 enabled on it (as best-practice guides advise, AFAIK) you'll also get that site-id conflict.
So i've got two L2-facing sites and there will be the third, over L3 in the near future. This is the reason to use EVI (as well as more efficient traffic paths using VRRP) and not just tag the VLANs through L2, if someone asks why did i configure it at all.
Hope this info will be helpful for someone.
P.S. And thanks for HPE guys who pointed me to right docs to undesrstand what is going on and the differences in evi in 7900.