I’ve found some messages from my boyfriend to his ex…?

We’ve been together just over a year and I’ve seen messages to his ex from 6 months into our relationship such as:
‘I miss you so much’
‘I dreamt about you’
‘I have so much feelings for you’
‘Do you want some new perfume’ (as he would buy her some when they were together)

At the same time of these messages we had met each others families, he was telling me he loved me and he asked me to move in with him.

I have confronted him about it and he downplayed it.

They haven’t spoken since January (as far as I know). But should I be worried?
I’ve found some messages from my boyfriend to his ex…?
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