I think I can confirm what the new change is. It would only appear 24hrs after your previous spin, and likely a little random even after the timing.
Example:
You got online and spin Trudy at 5am NST on Monday. Even if you get online at 1am NST on Tuesday, you won't be able to get it. Only AFTER 5am, and probably not immediately, will you be able to spin on Tuesday. Say you were only able to get online at 5:30am NST on Tuesday, the next timing for Wednesday is AFTER 5:30am NST. Thus certain people keep getting delayed into later and later timing because they aren't online for few hours straight.
This also explains why people keep saying they spun at 8am NST the day before but is unable to for the next. It's likely they didn't cared about the exact minutes and went offline after being unable to spin. This resulted in an even later timing for the third day.
Edited by neopetsexploded, 13 August 2015 - 10:03 PM.