Obviously, the Clintons wanted somebody from their wing of the party, somebody who wasn't in Bernie's (or Barack's camp), somebody who wouldn't throw their appointees out of office, some body who would let remaining Clintonites into the White House, but I doubt they would have been coordinated or powerful enough to tell Kaine what to do. Not with Bill looking like death warmed over. IMO, it wasn't so much that they thought Hillary would die and wanted a puppet they could order around. It was that they assumed she'd live and wanted somebody around who would give them the minimum of trouble and the smallest possible show of independence.
When I’m talking of Clintonistas there’s a generational aspect as well, not just the originals but their people they’ve groomed too.
The Clinton Foundation cannot be the only part of their machine, there has to be elements kept in place in the government that is able to preserve some influence whereby money and protection can be allotted. Those elements logically stand to benefit materially, eventually the power is theirs, or at least some of theirs. That’s how shadow governments happen.
For instance, do you recall Obama saying he wasn’t going anywhere? If he wants to be the kingpin of the DNC going forward then he likewise had to be about trying to get his people into place as rivals to Hillary’s. When he said he wasn’t going away he did so, IIRC, when it was still assumed that Hillary was going to be President. To the extent that it may be his in place resources causing Trump trouble rather than the Clintonistas they were being positioned to use were she in office.
I think the Clintonistas are ultimately about just the wealth and power, they are easy friends in collusion with the ChiComs. I look at Obama as being possibly more likely interested in the classical Leftist revolution motif, though with likely Muslim Brotherhood ties. I think that’s the struggle for the future of the DNC between them.