1) The Vampire was the only threat in the encounter.
2) The Vampire was the one from the MM straight.
3) 4 8th level PCs. The module says it is designed for 8th level PCs.
CR 13 vampire from the MM is 10,000 xp.
DMG deadly xp budget for four 8th level PCs is 8,400, so well into deadly territory. 10,500 xp is deadly for five 8th level PCs. 9,600 xp is deadly for four 9th level PCs and hard for four 11th level PCs. 10,00 xp would be in the hard range for four 10th level PCs.
Round 1 the vampire charmed the barbarian and the specific charm has this line "The charmed target regards the vampire as a trusted friend to be heeded and protected."
Three PCs attacking the CR 13 vampire and one protecting him is a bad start. A CR 13 monster on its own is considered a deadly encounter for three 11th level PCs.