Tobias and Emilia both believed they found true love in each other.  From Emilia's point of view, Tobias was her Prince Charming, who not only loved her, but provided a pathway out of the poverty that has weighed on her her entire life. But because she grew up so poor, and Tobias isn't really being forthcoming about how badly off his finances are after breaking the engagement, (and she doesn't have the mathematical ability to do the finances herself like Dahlia did) she thinks that for someone of Tobias'  assumed means, buying a replacement necklace is like "buy me a USB stick", when for Tobias, it's actually like 'buy me a new laptop."  It was a stupid, petty romcom shenanigan ruse, and it failed.