$push and $set in same MongoDB update

I don't know Java driver, but do you have to create a list there? What happens if you try this code?

BasicDBObject update = new BasicDBObject().append("$push", new BasicDBObject().append("values", dboVital));
update = update.append("$set", new BasicDBObject().append("endTime", time));

collection.update( new BasicDBObject().append("_id", pageId), update, true, false);

This should produce the equivalent of

db.collection.update({_id: pageId}, {$push: {values: dboVital}, $set: {endTime: time}});

Whereas your code produces (I suspect) this:

db.collection.update({_id: pageId}, [{$push: {values: dboVital}}, {$set: {endTime: time}}]);