If the whole house automatic TS is up stream of the portable Gen TS, such that the portable Gen TS is switching the upstream supply, be it POCO or whole house sourced, I don't see any issues with this configuration. The critical thing is the portable Gen TS must be positioned to switch the circuit regardless of the source (POCO or whole house), thereby preventing any possibility of feeding any circuit with more than one source.
I have a somewhat similar configuration, but use two backup sources...one a generator and one a battery inverter. I have a 4 circuit (4 switches) Transfer Switch 1 (TS1) and a ten circuit (10 switches) Transfer Switch 2 (TS2). TS1 decides between POCO and Inverter (mix or match among the four circuits). Those four decisions are feed to Transfer Switch 2 (TS2), along with six additional circuits. TS2 decides between generator and the other input. Six of the other inputs are POCO, and four are whatever is fed from TS 1 (POCO or Inverter). This allows me to mix and match the four circuits between gen, POCO, and inverter without any chance of a double feed.
In a nutshell, I have cascading Transfer Switches where the decisions are made in a sequence to physically avoid any possibility of feeding the same circuit with two power sources. A similar approach would work with an automatic whole house and a separate gen switch. Again, the key is the cascading nature of the two switches must ensure no possibility of energizing the same circuit from two sources.