Real or Personal Action

Yesterday, a question came up in class as to whether an action for foreclosure or partition is necessarily a real action. I just want to underscore that foreculosure and partition proceedings may not solely involve real but also personal property. I dug the following excerpts from SC cases which may be of help in cracking the question:

In Hernandez vs. Rural Bank of Lucena, Inc., the Court made the following distinction between personal and real action:

In a personal action, the plaintiff seeks the recovery of personal property, the enforcement of a contract or the recovery of damages.

In a real action, the plaintiff seeks the recovery of real property, or, as indicated in section 2(a) of Rule 4, a real action is an action affecting title to real property or for the recovery of possession, or for partition or condemnation of, or foreclosure of a mortgage on, real property.

Am I right to presume then that the determination as to whether the action is personal or real is necessary in order to determine jurisdiction? The court further ruled in Gomez vs CA [G.R. No. 127692. March 10, 2004] that:

Real action is one which affects title to or possession of real property. However, it does not automatically follow that the action is already one in rem. An action in rem is an action against the thing itself, instead of against the person while an action in personam is an action against a person on the basis of his personal liability. Hence, a real action may at the same time be an action in personam and not necessarily an action in rem.

Is it right to conclude then, that the determination of whether an action is one in rem or in personam or quasi in rem is not to determine jurisdiction per se but in order to meet the publication requirement of law as sine qua non for courts to acquire jurisdiction?