I have a character with the Izzet Engineer background and the spells from the backgrounds spell table don’t show up as known spells but will show up if I go on pc and prepare them

Which is correct.

Background spells do not add spells to characters, you don't instantly know them - it adds it to the spell list when choosing spells to know/prepare/add. So, if a "Known" type (e.g. Bards, Sorcerers, Warlocks): you can choose to add the spells when selecting your known spells. If a "Prepare" type (e.g. Clerics, Druids): you can prepare the spells when you prepare your spells. If a "Book" type (Wizards): you can choose to add the spells to your spellbook when appropriate to do so. 

Apologies maybe you misunderstood or I explained incorrectly, but the spells do not appear in any capacity anywhere on mobile unless I go onto my PC where I can see them in my known list and add them there from my known spells to my prepared spells.

Quote from StanleyAllen >>

Apologies maybe you misunderstood or I explained incorrectly, but the spells do not appear in any capacity anywhere on mobile unless I go onto my PC where I can see them in my known list and add them there from my known spells to my prepared spells.

Oh, that is different.

On Home page of the character builder enable the Magic: The Gathering toggle.