Dear Adrian,
You must think about how the bottles were produced and then sold.
Many bottles, possibly at times, most bottles produced by a specific artist, were produced on order.
A customer/collector came in, negotiated a deal with the artist, based on material of blank [quartz/glass], and level of painting [superb quality down to standard quality], and the inscription desired [a personal dedication for a collector; a dedication to a superior if meant as a gift/bribe/etc.]. These would all have had inscriptions including the artist's name and a seal at the very least.
But all artists at the start, and often later, had free time on their hands, and would produce 'sales stock', because it was their livelihood, and also in case a buyer walked in and needed a bottle 'in a hurry'. And the artist would have been aware that there were buyers at all levels in this situation, so he would have had bottles that were unsigned, at all levels.
These bottles were left unsigned so that the inscription would look 'original' - ie., so it would NOT look like the artist had signed it in 1895, and added the rest of the inscription in 1899.
So either these bottles were still unsigned [and thus unsold] by his passing, presumably in 1918, when his work stops; or possibly, Yan Yutian sold unsigned bottles or gave them as gifts to friends, and didn't bother to add an inscription.
For a Bar Mitzva or Wedding gift, he'd have added the inscription; for lunch at a friend's, possibly not...
The reason I am conjecturing all this [and it IS conjecture on my part], is because I have a number of friends who are artists in Israel, the UK, Ireland and the PRC, and I've noticed that they all have paintings / snuff bottles / silver objects / bronzes / etc., that are finished but unsigned.
The silver is hallmarked, a legal requirement; but the artist then inscribes it with personal info [name/date/etc.] on the base with a scribing tool.
Best,
Joey