Hong Kong is a Day ahead of Cuba. In your case 13 hours. From 2:08 PM to 3:08 AM.
Something in your iPhone did it not LR Mobile.
What exactly were the steps you took to make those two copies of the same image? Their EXIF DateTimeOriginal (the capture date) are different by 13 hours, which as Just Shoot Me points out, is the difference in time zones between Hong Kong and Havana. But without knowing the steps you took to make those two copies, we can't tell whether it was LR Mobile or iOS Photos or some other app that changed the date.
In LR Desktop, you can use the Metadata > Edit Capture Time to shift the times of a batch of photos all at once.
(1) In my recent Cuba trip, I took some images with my iPhone 6S. All the images were edited with Lightroom Mobile and saved in the Camera Roll in 6S. The first image shows what I got from the Lightroom APP and the second images shows the information of the JPG photo saved in the Camera Roll.
There are some other images with EXIF of Cuba of this trip :
(2) As the images were edited with the previous version of Lightroom Mobile, all the images are of lower resolution. When I came back to Hong Kong, I saved these hundreds of images in full resolution in Camera Roll again. But this time, the Lightroom APP shown is as the third image. The new images in the Camera Roll are with a different capture time. I just wonder why the capture time of the images will be changed with the time zone ?
(3) Now, I reset the time zone to Havana and save my images in Camera Roll again even I AM IN HONG KONG.
(4) To keep my trip simple and light, I usually don't bring any notebook with me. All the editing of the photos are done in my iPhone 6S.
(5) As re-save these thousand of images is a time wasting work, I try to sync the image to my Mac Power Book through the Creative Cloud in Hong Kong. What I got from my Lightroom APP in my iPhone 6S is "Uploading ... 637 Pending..." This last for three days and still stays here.
From your more detailed description, it sounds like it's the LR Mobile app that's changing the date/time of the photo as you change time zones, but I can't be positive without doing a lot more investigation. You might post a problem report in the official Adobe feedback forum, including all the detail you've provided here: Photoshop Lightroom | Photoshop Family Customer Community. Don't just link to this thread, since the Adobe product developers would be less likely to pay attention.
In general, the photo industry has long made a hash of handling time zones. LR Desktop has decided, not unreasonably, to try to ignore them entirely, being careful to not change capture date/times (unless the user explicitly changes them). Unfortunately, it wouldn't surprise me if LR Mobile has bugs or misfeatures in its handling of time zones.
What I got from my Lightroom APP in my iPhone 6S is "Uploading ... 637 Pending..." This last for three days and still stays here.
I've seen other threads in this forum about that issue. You might search for them. If you don't find anything relevant, start a new thread, so others who might know more about that issue will be more likely to notice.
There's a definitely a bug in LR Mobile with respect to changing time zones. I filed a detailed bug report: Lightroom Mobile: Incorrectly adjusts capture time when time zone of phone changes | Photoshop Family Customer Community. Please add your vote and opinion to make it more likely that Adobe might fix the issue.