I tried the: getTime.sh ; hwclock --utc --systohc command but got an error message: hwclock: can't open '/dev/misc/rtc': No such file or directory. After what I can see TC uses the hwclock time on this computer which is UTC+2 with daylight savings time (otherwise UTC + 1).
The hwclock command failed because I forgot to tell you to use sudo. Do not execute that until you have tried a few more tests.
Boot your system and execute
tce-load -wi ntpclient.tcz ; ntpclient -c 1 -h pool.ntp.org | awk '{print $5/(60*60*1000000)}'
which will report the number hours that your system clock is offset. My guess is that the offset will be about 2 hours, which corresponds to the difference between your local time and UTC.
Boot your system again with the noutc bootcode (tinycore noutc ...) and execute the same commands. My guess is that the offset will be very small.
What I believe is happening is that the Tor Browser script is having to make a large adjustment to the system time because you did not include the noutc bootcode to tell tinycore that the hardware clock is using local time instead of UTC. If I am wrong about that, please report what the showbootcodes command prints.
If you decide that you would like to change your hardware clock from local time to UTC, execute
getTime.sh ; sudo hwclock --utc --systohc