When I set an export PROMPT_COMMAND, it changes my terminal settings?
The problem is that PROMPT_COMMAND is used by the system bash to enable per-session history. If you look at /etc/bashrc_Apple_Terminal you see

# Note that this uses PROMPT_COMMAND to enable per-session history
# the first time for each new session. If you customize PROMPT_COMMAND
# be sure to include the previous value. e.g.,
#
#   PROMPT_COMMAND="${PROMPT_COMMAND:+$PROMPT_COMMAND; }your_code_here"


So if you want to follow the recommendations in the advice you've linked to you are better off just using

export PS1="\t [\u@\h \W]\\$ \[$(tput sgr0)\]"


or similar. If you really want to use PROMPT_COMMAND

PROMPT_COMMAND="${PROMPT_COMMAND:+$PROMPT_COMMAND; }echo -n \[\$(date +%H:%M:%S)\]\ "


but the prompt will get messed up if you navigate back in time with Ctrl-P.