Direct to pool or VS based on logon domain

You can use VPE pool assignment (from pool assign help)

Pool Assignment

In a per-session policy, the Pool Assign agent enables session-based pool selection from among valid pools in this priority order: a pool selected by an iRule that is defined for the virtual server takes precedence over any other; a static pool defined in the Pool Assign agent takes precedence over a static pool defined for the virtual server.

In a per-request policy, the Pool Assign agent enables request-based pool selection for reverse proxy (LTM+APM) configurations only. In a per-request policy, the pool specified by the Pool Assign agent is assigned.

or use an irule

when ACCESS_ACL_ALLOWED {
    if {[ACCESS::session data get session.logon.last.domain] equals Domain_A} {
        pool pool_A
    } else {
        pool pool_B
    }