Before the chemistry lesson:
On its own, tomato paste has an offensive, raw taste with a somewhat bitter aftertaste (a result of sulfur derivatives). You need to cook it to get "the raw" off it. Heat makes for a particular kind of good flavor chemistry. However, in brown sauce a.k.a. sauce espagnole paste is not there for flavor -- at least not much. It's there to provide structure. If your espagnole tastes like a tomato sauce, than it's got too much tomato. The taste of tomato should be barely recognizable.
The right way to cook tomato sauce for an espagnole, as for most sauces which aren't going to grow up to be tomato sauce, is by creating something called a pincage in French. As far as I know it has no name in English. After the aromatics are nearly cooked, you push them aside to make a space in the pan, and add the tomato paste to the space. Let the paste sizzle long enough to form a fond on the bottom of the pan, then move the aromatics through the paste to coat, and cook until the color darkens. Et voila! Pincage! At that point, you remove the Gauloise from your Gallic lips, give a Gallic shrug, add flour to make a roux, stirring only in the clockwise direction, every stroke circumscribing a well deduced metric diameter.
With all due respect, AFAIK, Luc's description does not cover the chemistry as it is understood. What you're doing is not "enhancing" a Maillard reaction later, but creating one (or something very much like one) in the paste itself. Bitter, starchy, raw to sweet, deep and finished. "In tomato paste, for example, it was found that changes in aroma [and taste] caused by heating are primarily caused by the formation of dimethyl sulfide, methional, the furanones HD2F and HD3f, and the increase in [beta-]damascene and a substantial decrease in (Z)-3-hexenal and hexanal." [emphasis added] (Food Chemistry by Dieter-Blitz, et al). If you know your food chemistry you know that the furans and damascenes are your friends. IIRC, They are the product of a Maillard or Maillard type reaction, rather than an intermediate step.
Indeed, the raison d'etre of an espagnole is to infuse "browning" and structure into stock. That's why we cook the raw off tomato paste.
I hope everything, now she is clear. Eh, mon ami?