You are correct: it’s an additional spell, separate from the one that triggered the Wild Magic Surge.
This ability is triggered when you use a Metamagic option, which for all but two options, trigger when you cast a spell; Empowered Spell triggers when you roll damage for a spell, and Seeking Spell triggers when you make an attack roll for a spell and miss. In all cases, any trigger that would take effect when a Metamagic option is used would take place at least after the initial spell has finished casting. This means the potential resulting spell from a Wild Magic Surge coming from the Feywild Shard would take place after the effects/concentration of the initial spell have already begun, and would not retroactively cancel the previous spell.
Also of note, the same statement is mentioned in the Wild Magic Sorcerer’s Wild Magic Surge feature ((PHB p.103)(2)):
If that effect is a spell, it is too wild to be affected by your Metamagic, and if it normally requires concentration, it doesn’t require concentration in this case; the spell lasts for its full duration.
This is referring to the Wild Magic Surge