Whether that first subscriber themselves considers the thing they've bought "dark fiber" or "lit fiber" once they light it up, depends on if they're made an exclusivity agreement with the provider. If they have, then the fiber is still "dark fiber" from their own perspective. If they haven't, then the fiber should be considered "lit fiber", because now that it's been set up for their use, the provider has likely put it on the market for others to lease as well, so it's not going to stay "dark" for long.
But really, these are silly terms. Customers don't care about buying "dark fiber" vs "lit fiber"; they care about buying "dedicated fiber" vs "[dedicated throughput on] shared fiber." (A lease on dedicated fiber allows for nearly-arbitrary throughput scaling over time at no additional OpEx — just the CapEx of upgrading the transceivers on either end once-a-generation or so.)
The only two things that you know by buying "dark fiber" from a peering provider, are:
1. Demand for that path was lower than predicted at the time you requested it, so there existed at least one fiber-infrastructure developer who had run some fiber along the path but not managed to sell it off to any particular peering provider yet. (Peering providers don't tend to buy-and-hold fiber without either immediate or predicted base-load demand; rather, they index available-to-purchase fiber from infra developers, offering those to their customers at snapshotted rates; they then buy the fiber from the developer in response to a customer Purchase Order, eating any loss from purchase-price volatility.)
2. You might have to pay the peering provider you're leasing from, for the initial set-up work of lighting up the fiber: routing a secondary fiber link from the optical switch in the fiber-infra developer's overland or shoreside termination point, over to the peering provider's cable hotel; terminating that fiber into a [maybe fresh] optical switch or transceiver in the cable hotel; etc.