1)
Why did David expect to see Mefivoshes?
1.
Malbim: David assumed that Mefivoshes commanded Tziva to bring the gift. If so, why did he stay in Yerushalayim? Avshalom will kill him when he finds out! Tziva said that he himself sent the gift.
2)
Why did he say that Mefivoshes stays in Yerushalayim?
1.
Malbim: He did not go to greet Avshalom, nor to flee with David. He plans that Avshalom will kill David, Yisrael will judge him like a Ben Sorer u'Moreh, and kingship will return to Beis Sha'ul.