What was the miniature - was it resin, or plastic, or...?
Also, it's a known issue with many inks (and some acrylic paints with strong pigments like dark blues and dark greens) that they reactivate with certain brush-on varnishes and bleed their colour into the wet varnish. In particular, old GW inks, W&N inks, and a few others are very prone this.
To avoid shiny inks, I recommend adding a little bit of matte medium to them on your palette before putting them on the models. This will make the ink dry matte.
For sealing, I would use a good water-based polyurethane varnish (find one that is both UV-resistant and non-yellowing from a trusted brand like Ronseal) and do a thinned gloss coat first. Afterwards when dry, do your matte varnish coat of choice - the gloss not only protects your models better, it also acts as a sealing layer between the paint and the final matte finish.
If you happen to be using Reaper Bones or similar soft plastic figure, then I'm afraid the problem is the material from which the miniature is made, not the paint/ink or varnish.