Edit
Interestingly, when I went to go grab the LR to record the video, I left the cord I was using for power in the other room (the same cord I have been using since I first for it), and grabbed a different cord for power, I have done probably 150+ presses and have only seen the delay 2 times so far.
I had just recently moved it into another room, so I brought it back to my desk and plugged it in. I don't recall the issue being time-related (in that it's fine at first, but then later it starts acting up), so I will keep an eye on it throughout the rest of the day, testing now and then and report back tomorrow.
I appreciate the reply. Yes, the delay is indeed reflected in the light flashing on the device itself.
I have the LR on my desk in front of me sitting on a little 5 port switch, so I am able to clearly see the light and the delay in the light flash coincides with the other findings I mentioned above.
I had opened and connected one of my Twist devices as soon as it arrived after the Kickstarter and the delay existed then (on whatever the LR firmware was at that time).
My second one, I only recently opened and connected the day you replied to my message in another thread about the SDK/feature update being available for Android. Both of these devices experience the same delay to the hub as of now (just tested again a few seconds ago with the 'newer'/just recently opened device) on firmware 4.4.2.
As for usage, I have a virtual light device setup on each, and rotation and press values are sent via mqtt, and there is a subscription setup to listen for current value to update the led. Prior to that (1 or two years ago, I can't say for sure), at some point I did setup the button press through the app to send an HTTP request. The delay happens the same no matter how I use the device, and seems to occur before any user code/actions are performed.
I was going to open the SDK console and using my phone, record a clip where the button, the hub itself (and light), as well as the console are all in frame so when I press it, the delay can be seen in realtime but wasn't sure how useful that would be.