The Democratic Republic of Georgia was led by Mensheviks whose interest before 1917 had primarily been in all-Russian Social Democracy. They chose independence only because they really had no choice after the Bolsheviks took control of Russia and the short-lived "Transcaucasian Republic" disintegrated. I would not call a government for which national independence was a last resort "nationalist." As for "imperialist" the most that can be said is that it did have some border disputes--something inevitable under the circumstances. But it's not as though they were trying to restore the borders that existed in the reign of Tamar.
Some border disputes might have been understandable. Still, there's the sheer number of them, and the fact that they all invariably involved Georgia trying to subjugate non-Georgian regions.
The Georgian government was very much infected with the universal nationalist love for ancient borders and so-called "historical rights". I don't know if they specifically used Queen Tamar, but they did constantly try to justify their imperialism by recalling the borders of medieval Georgia, the projects of King Iraklii II and other such relics from the past.
To that we can add
-sealing the borders in front of Armenian refugees (refugees from an area claimed by Georgia, no less), leading to the death of 30,000 of them;
-Blocking the transit of grain to Armenia (which was already suffering extreme starvation) in order to more easily enforce its opportunistic seizure of Armenian territories;
-colonization of Armenian-inhabited lands with Georgians;
-ethnic cleansing against the Ossetian population and colonization of South Ossetia with Georgians
and so on.
A quote David Lang (
A Modern History of Georgia), which I strongly agree with:
"It is ironic to observe how the Georgian Social-Democrats, whose leaders were working as late as 1918 for the triumph of democratic socialism in a Russia united and undivided, were at length transformed by the force of circumstances into nationalists of chauvinistic fervour...". 'Menshevik' Georgia might not have been born nationalist, but it very quickly descended into a virulent ultranationalism.