What the cursor keys send depends on the keyboard mode.
tput
reports their application mode value but by default, the keyboard is in standard mode.
The DEKCKM command can be used to just change they cursor key behavior, example:
printf "\033[?1h"
or you can use the smkx
command which set the keyboard to application mode:
tput smkx
Reset with:
printf "\033[?1l"
or
tput rmkx