Yes, your understanding is correct and this behavior is expected given how Mixpanel's attribution and filtering work.
When you use a first-touch attribution model with a 30-day lookback window, Mixpanel credits the earliest touchpoint within that window for the conversion. In your holistic report (with all channels included), the first touchpoint is email, so email receives the credit.
However, when you filter the report to only include paid media channels, Mixpanel excludes email from consideration. In this filtered dataset, the earliest remaining touchpoint is Google Search, so it becomes the new "first touch" and is credited with the conversion. This is consistent with how Mixpanel's attribution filtering works: after applying an attribution breakdown, filtering narrows the total conversion events to only include/exclude those with the associated attribution property. If a touchpoint is filtered out, the next available touchpoint in the lookback window is used for attribution, as you described.
This is documented in Mixpanel's attribution FAQ:
Once attribution is computed, filtering narrows total conversion events to only include/exclude those with the associated attribution property... You can apply a filter on an attribution property only after an attribution breakdown has been applied.
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For example, if you want to look at only Purchases that have come from a non Direct Channel, only those purchases with non-direct channels as the last touch will be included.
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You can apply an attribution filter only on the property used in the attribution breakdown
Docs: Attribution FAQ
So, when you filter out email, Google Search becomes the first eligible touchpoint and is credited accordingly. This is expected behavior in Mixpanel's attribution analysis.
