Thank you. That additional information was helpful.
I am not an expert on Dutch trains, so I really hope someone else can step in to provide certainty.
I tried selecting both the direct option and a couple of the options requiring connections, and the follow-up screens showed the same "Order Overview", just specifying the origin and destination. I suspect you'd be OK taking any of the listed departures for which PriceTime tickets are available within the travel window specified on the follow-up screen. However, the website info isn't totally clear to me, either.
What you might consider doing is selecting the departure you currently prefer, buying the ticket, and then inquiring at the first practical train station. There should be no problem getting clarity there, because the Dutch speak excellent English. Odds are you'll find out you do have the desired flexibility. If not, you'll know ahead of time which train you must take. In event of a serious scheduling conflict, you could just buy a new, full-fare ticket.
You could also use the chat function on this webpage: https://www.ns.nl/en/service-and-contact
Thank you for posting this question. When I saw an occasional PriceTime offer last year, I assumed I had to take the specific train I chose, so I never took advantage of the discount.