Other replacement effects that would change the number of loyalty counters Jace enters with will apply as normal.

Jace's second loyalty ability doesn't care which player's graveyard has twenty or more cards in it. It could be the target player's or another player's.

A Phyrexian mana symbol contributes 1 toward the mana value of a card, even if life is paid for it. Specifically, Jace's mana value is always 4.

The compleated ability looks only at whether a player chose to pay 2 life for a Phyrexian mana symbol as they were casting the spell. If a player paid life for some other reason while casting the spell, that will not reduce the number of loyalty counters the planeswalker enters the battlefield with.