Well I tried to test it with my
***WINNER*** video where he used a lot of Wand of Speed and I still had my save (which means access to my characters' speed).
At 9:29 He used HP restoring medicine, which has a post-use of 2500 (meaning 7500 to next turn). After this turn he had a SPD buff of 25%.
If SPD buff affects player speed, he would have 3540 * 1.25 = 4425 player speed, which means 980 effective speed, which means it takes 8 CT to get his next turn.
If SPD buff affects actual speed, he would have 880 * 1.25 = 1100 effective speed, which means 7 CT to get his next turn.
One CT after, Minoriko, who has 2115 player speed (685 effective speed) used Wish for an Abundant Harvest, which has a post-use of 5000, meaning she needs 8CT to get her next turn.
A bunch of stuff happens in the next n (6 or 7) CTs, then WINNER receives his next turn and uses Sword of Light, but Minoriko survives. On the next CT Rinnosuke gets his turn, but Minoriko still hasn't gotten hers yet. Since there is at least two CT between the Sword of Light and Minoriko's next turn, it follows that it took six CTs for WINNER to get that Sword of Light turn after Minoriko's heal, which means he took 7 CTs between HP-restoring Medicine and Sword of Light, which means that SPD buff affects actual speed.
Now it's possible that not 1 but 2 CT happened between HP-restoring medicine and Minoriko's first turn, and I really don't have definitive calculations to support that (I don't really feel like running through the entire video just to calculate what CT the battle is on). However, if you rewind the video by two turns (WINNER's moves were Wand of Speed -> Ringil -> Sword of Light -> HP-restoring Medicine -> Sword of Light), when Wriggle gets her turn between WINNER's Ringil and Sword of Light, his gauge looks pretty much full enough to get his next turn on the next CT (at that point he had 40% SPD buff, which means over 1000 effective SPD either way). Sword of Light at 32% is 6 CT regardless, and Wriggle then performed two switches in a row (she had 2705 SPD which means 772 effective speed, so 4 CT per switch), with Minoriko getting her heal turn on the same CT as Wriggle's turn after her second switch, so it really makes sense that this particular point in time is only one CT after HP-restoring Medicine.
tl;dr version of (what I thought) the flow of clockticks:
CT0: WINNER uses Ringil. (4CT)
CT3: Wriggle performs a switch. (4CT)
CT4: WINNER uses Sword of Light. (6CT)
CT7: Wriggle switches Minoriko in. (4CT for both Wriggle and Minoriko)
CT10: WINNER uses HP-Restoring Medicine. (7CT if SPD buff affects actual speed, 8CT if SPD buff affects player speed)
CT11: Minoriko uses Wish for an Abundant Harvest. (8CT)
CT17: WINNER uses Sword of Light.
CT18: Rinnosuke gets a turn here, indicating that Sword of Light happened before CT18, which infers that his 25% SPD buff affected his actual speed.