The aphids on your hollies are likely holly aphid (Aphis ilicis) or a related host-specific species. Most aphids are host-specific—they feed on one or a few related plants.
Generalist aphids (green peach aphid, melon aphid) can feed on many plants, but they're not the ones on your hollies.
Host specificity is why aphid "outbreaks" stay on one plant type. Your other plants aren't at risk from the holly aphids.
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