I will give a clear example:
Unique. Elf. Manifestation of Elrond. One strike. Detainment against hero companies. As a creature, may be played keyed to Rhudaur, Arthedain, High Pass, The Shire, or Cardolan; or at sites in these regions. As a permanent-event, each player at the end of each turn may bring one Elf creature from his discard pile to his hand. Discard when any play deck is exhausted.
The question is simple:
I have 7 cards in my hand at the "beginning of my end-of-turn" phase, the reason that is in quotes is because I am not talking about Saruman's E-o-T phase effect at the "beginning", or similar. Just an effect that states similar to the above in bold, at the end of each turn.
So back to the question, I have 7 cards at the beginning, and I choose to discard a card going down to 6. I now draw up to 8 cards, base hand size, then the Master of the House effect triggers, and I am at 9 cards.
i.e. Just like I can play a Longbottom Leaf after I reconcile and end up with 7 cards, I can also, get an Elf, and end up with 9, or even go so far as to end up with 10, if The Nazgûl are Abroad is in play, by grabbing a Nazgûl Creature/Perm.
Thanks for confirmations!
n.b. just gotta pay attention to which effects are at the Beginning of the EoT phase, and which ones are at the EoT.
