Here is a not great workaround:
(defun my:tooltip-by-point (msg)
"requires fullscreen to position correctly"
(interactive)
(let ((left (car (window-absolute-pixel-position)))
(top (cdr (window-absolute-pixel-position))))
(x-show-tip
msg
(selected-frame)
(append `((top . ,(+ top 410)) ;; 410 found by trial and error
(left . ,(- left 205)))
tooltip-frame-parameters)
tooltip-hide-delay
nil nil))) ;; DX DY irrelevant due to PARMS containing `top` and `left`
It requires the "magic numbers" 410 and 205 to adjust for some sort of offset that is occurring. You may need to adjust these numbers.
C-h f tooltip-showand note that it says "...Otherwise, the tooltip pops at offsets specified by 'tooltip-x-offset' and 'tooltip-y-offset' from the current mouse position" (emphasis added). That's because the function is not usually evaluated by hand - instead, it is called as a result of some mouse action, so it makes sens to keep the tool tip next to the mouse cursor.