You are right. It is at the “tanha paccayā upādāna” step that we do the both of the following:
1. We accumulate more kamma (and add to existing kamma bija).
2. We also grasp a new bhava at the cuti-patisandhi moment by “attaching to an arammana” via “tanha paccayā upādāna” which lead to “upadana paccaya bhava”, i.e., to a new bhava. Here an existing “kamma bhava” becomes “uppatti bhava”.
See, “Difference Between Tanhā and Upādāna” and “Taṇhā Paccayā Upādāna – Critical Step in Paṭicca Samuppāda“