Do animals summoned by magic items, such as the robe of useful items or the marble elephant figurine of wondrous power, follow player commands, Or are they wild animals? Or is this up to the DM's decision?
Yes for the Figurines of Wondrous Power. No for the Robe of Useful Items.
From the description of the Figurine of Wondrous Power found in the DMG (Dungeon Master's Guide) or the Basic Rules (page 169).
The creature is friendly to you and your companions. It understands your languages and obeys your spoken commands. If you issue no commands, the creature defends itself but takes no other actions.
From the same source (Basic Rules 195), for the Robe of Useful Items:
While wearing the robe, you can use an action to detach one of the patches, causing it to become the object or creature it represents.
The source doesn't specifically say that the creatures created by the item have anything other than what could be regularly found in their stat blocks, which is in contrast to the Figurines of Wondrous Power's description.
They do what the item says they do.
The Robe of Useful Items creates a Riding Horse (per the Player's Handbook) and/or Mastiffs (as per the Monster Manual). These are actual creatures of the type and are appropriately trained (so, not wild) but have no particular loyalty to anyone although this can be gained as it would for normal animals.
The Figurine of Wondrous Power says:
The creature is friendly to you and your companions. It understands your languages and obeys your spoken commands.