Theorically both tenses are possible , especially as the letter V was used at once to write the consonant and the vowel U in the Latin world and beyond. But as the tattoo of a regiment standard maybe you are right to prefer the present tense.
By the by this flag can be seen HERE ( the fourth on the page )
My dictionary lists solvi as the perfect, but admits exceptions soluit and soluisse from literature. I'm not sure how we know since the Romans did not distinguish u and v, but I suppose if it were in poetry there would be a metrical tipoff.