SQL Server Mirroring kicks in before cluster has time to fail over

I have two clusters each with two nodes configured in active/passive; the two clusters take part in a high-availability mirroring session using a separate server as the witness.

When a node fails in the primary cluster, the mirroring failover seems to kick in before the secondary node of the primary cluster has had time to come online.

Is there anyway of telling the witness server to let the passive node attempt to come online before initiating the failover to the secondary cluster?

Database mirroring questions from TechEd: failovers and partner timeouts

... when the cluster is failing over and the principal instance is
unavailable for 60-90 seconds, the other instances in the mirroring
session will time-out after ten seconds and initiate a mirroring
failover... The solution to the problem is to change the partner time-out value - a facility that isn't well known. To change the partner time-out value for a mirroring session, use the following code:

ALTER DATABASE mydatabase SET PARTNER TIMEOUT 90;

StackExchange Database Administrators Q#23111, answer score: 8