The Aes Sedai didn't know more than rumours-hearsay about this effect of stilling, because stilled women are shunned, and no one ever made stilling the subject of a study. Very few stilled women have remained around to be seen either (Bonwhin was one such exception, but as a scullion and probably no Aes Sedai wanted to take a good look at her).

Obviously, the loss of the ageless look cannot be instantaneous nor even close to, because then it would be common knowledge that stilled women look like this (we know it's customary, perhaps even law, that AS in the Tower attend the major punishments - and of course there are those carrying the sentence too). One thing is that the sentence of stilling in Tower Law is most often symbolic and ritual. Sisters are stilled, to strip them of their ability to channel and thus of their status as Aes Sedai, before they can be executed. This way, it's never sister who is executed. Before capital punishment, the sister is forsaken from the Tower (a tradition that may date back to the WOS, when the evil Aes Sedai were stripped of status and even renamed in scorn, and called Forsaken)

If Siuan had lost her ageless look anywhere near instantly, it would have been noticed by the women who carried the sentence and then, once she was stripped of her Aes Sedai status, put her ruthlessly to the Question through the night (which, by Tower Law, they cannot do to Tower initiates, even suspected BA. As the BA hunters pointed out, they could have been stilled for putting Talene to the Question, because Talene had not been stripped of her AS status. So Siuan was judged summarily, stilled then put to the Question).

Logically, Siuan only began to lose her agelessness look over the hours after her stilling, and there's no very solid evidence that it didn't fade gradually over a longer period of time (though it's unlikely, given how the ageless look is a kind of OP skin streching). The next day she already didn't look like the Siuan of old, but we don't know if she already had her "final" new look then, or if she kept changing for a while.

What we can surmise from the episode and what we know is that it begins right away, but it takes many hours to start being really noticeable, and perhaps days before the process is over and the woman is back to her natural appearance (that is, Siuan and Leane look like women of fairly high strength, who began channelling early around 16 y.o and thus would start to slow early, would look in their mid-thirties. That's fairly good evidence that a removal of the Oaths by stilling or with the OR simply negate the side-effects of binding on your body, and you're back to your natural appearance. In other words, it means the "ageless look" is "faked" - a OP equivalent of a lifting... If you release the net from the binder, what kept your skin streched is removed and you gradually regain your real appearance. The rest of the "agelessness" is due to the fact the Aes Sedai lifespan is cut by half. The real signs of decay, health loss etc. happen past your middle years, and all bound AS die suddenly before that phase of their life. Unbound very old channellers we've seen reach a point where their body decays (Cadsuane's toothless wilder), become frail (the Rhuidan AS) and very likely they can get sick like any very old people - very strong evidence that Aes Sedai's "immunity" to diseases is a Tower misconception is the middle-aged Mesaana's fears of this Age's diseases. The OP may give them some protection, like a boost of their immune system, but the "magical" health of the Tower's AS is by and large due to the fact very few of them seems to survive past what would be comparable to the biological age of 30, 35, 40 y.o. Cadsuane, at around 300 (so around 50 y.o., a 50 y.o. who's kept active and in good shape all her life at that) is presented as really exceptional. A lot of sisters seem to die closer to their 200 y.o., which is comparable to 30 y.o. for a woman of Cadsuane's lifespan (and unbound, it means these women would have died at a point comparable to their early or mid sixties)