Your understanding is correct. The following section taken from the Synchronised Database Service white paper suggests there is no automatic restart of server applications following a negotiated or hostile takeover of the primary node:
Preparing for a Takeover Operation
Prior to performing a takeover, the following steps are recommended:
1. If the reason for the takeover is to perform scheduled maintenance on the primary host, then it’s preferable to shut down all nodes connected to the primary before initiating the takeover.
2. When possible, shut down all update-capable processes on the primary database. Stopping update processing ensures there are no active transactions when the takeover is initiated – a database quiet point on the primary is a prerequisite to the takeover action. If updating applications are left running on the primary system, they will encounter exceptions next time they attempt to update non-environmental objects once the primary database has assumed a read-only secondary database role.
On the other hand, there is no real need to stop inquiry processes on the secondary that is to assume the primary role. As soon as the takeover is accomplished and the secondary has changed roles to a primary, the inquiry processes can begin to perform updating transactions without the need to restart.
Interestingly PAR #30003 corrected an issue in JADE where server applications would automatically restart following a negotiated takeover, but this was changed so:
...that it is more discerning about when to start auto ini apps. It will only attempt to start them when database access is FIRST enabled i.e. as a result of an SDS Secondary Server Node being started.
An NFS could be opened against JADE for a user takeover option, such as "StopServerApplicationsOnTakeover=true". This could allow the developer to design the server application without having to include support for possible role and therefore access changes, and the operator to have one less task to do when performing a take over. Similarly for starting server applications.