Persistence causing problems with redirection iRule?

You're missing a else-clause (default action) in your iRule. In other words, once a request lands in your test pool, there's no way to return to default pool (since the balancing decision is already locked in).

when HTTP_REQUEST {
   Save the name of default pool (as configured in VS Resources Tab) as a variable, before it can be modified by conditional actions below
  set poolDefault [LB::server pool]

  if { "[HTTP::host][HTTP::uri]" starts_with "www.website.com/test" } {
    pool test_pool
  } else {
    pool $poolDefault
  }
}

Similar problem here: https://devcentral.f5.com/questions/incorrect-load-balancing-when-disabling-oneconnect