It's as Bedwere says, Little Flower: "suus -a um" is reflexive, referring to the subject of the sentence. "Eius" isn't. So I hazard:
"Is Julius's servant here? His servant is." [And not: "His own servant is here."]
"There is no money is his bag, his bag is empty." [the comma here confuses me!]
Just think about resolving any ambiguity by imagining "his own and not anyone else's" = "suus -a -um".
Ut dicit Bedwere, Floscule, "suus -a -um" reflexum sensum habet, id est, sententiae ideaeve subjectivo refert; "euus -a -um" irreflexum, id est, alio quÃ m subjectivo refert.
ErgÃ´, ut puto,
"adestne servus iulii? servus eius adest."
"in sacculo eius pecunia non est, sacculus eius vacuus est."
[Haec comma me conturbat!]
Casu ambiguitatis, ostenditur quÃ²d "suus -a -um" congruens est.
Little Flower wrote:the first one seems to be saying that his (somebody elses servant) is present.
The subject of the verb "adest" is NOT Julius, it is "servus", so use "eius". Otherwise, "Julius dicit servum suum adesse", "Julius says that his [own] servant is present."