As mentioned by @JonatanLindén, fill-prefix is set to a string containing 18 spaces. This is because bibtex-clean-entry is using fill-prefix to align continuing text after equal sign. Setting fill-prefix to "" can solve the indentation issue. But to have better alignment when formating entry, you can advice bibtex-clean-entry to temporarily set fill-prefix.
(defun bibtex-mode-setup ()
(setq-local fill-prefix ""))
(add-hook 'bibtex-mode-hook #'bibtex-mode-setup)
(defun bibtex-reset-fill-prefix (orig-func &rest args)
(let ((fill-prefix (make-string (1+ bibtex-text-indentation) ? )))
(apply orig-func args)))
(advice-add 'bibtex-clean-entry :around #'bibtex-reset-fill-prefix)