The "intervening 'if' clause" means that (1) the ability won't trigger at all unless you control a permanent of the specified color, and (2) the ability will do nothing unless you control a permanent of the specified color at the time it resolves.

Normally, when a token is created by this ability, it will simply be a Mirror-Sigil Sergeant, so it'll also have the token-creating ability. (See the other ruling for weird exceptions.) At the beginning of your next upkeep, if you still control the original Sergeant, the token copy, and a blue permanent, you'll get two more token copies; the turn after that you'll get four; then eight; and so on.

Here's the detailed version of what happens. As the token is created, it checks the printed values of the Mirror-Sigil Sergeant it's copying -- or, if the Mirror-Sigil Sergeant whose ability triggered was itself a token, the original characteristics of that token as stated by the effect that put it onto the battlefield -- as well as any copy effects that have been applied to it. It won't copy counters on the Mirror-Sigil Sergeant, nor will it copy other effects that have changed Mirror-Sigil Sergeant's power, toughness, types, color, or so on.

If Mirror-Sigil Sergeant has left the battlefield by the time its triggered ability resolves, you'll still put a token onto the battlefield. That token has the copiable values of the characteristics of Mirror-Sigil Sergeant as it last existed on the battlefield.

Here are the weird exceptions. If any copy effects have affected the Mirror-Sigil Sergeant whose ability triggered, they're taken into account when the token is created. For example: -- If Mirror-Sigil Sergeant's ability triggers, then Mirror-Sigil Sergeant temporarily becomes a copy of another creature before its ability resolves (due to Mirrorweave, perhaps), the token will be a copy of whatever creature the Mirror-Sigil Sergeant is currently a copy of. After the turn ends, the Mirrorweaved Mirror-Sigil Sergeant reverts back to what it was, but the token will stay as it is. -- If the copy ability of a creature (such as Cemetery Puca, perhaps) makes it become a copy of Mirror-Sigil Sergeant and gain another ability, the token created by this creature at the beginning of your upkeep will be a Mirror-Sigil Sergeant with that additional ability.