Tags are organized alphabetically by the platform, so the Collection page filters would also follow this sequence. With Empire, use this theme editor feature to reorder groups and reorder tags according to your own sequence.
Go to Customize > Open a Collection page in the right-side preview > Open Collection pages in the left-side settings > Scroll down to the Group order field
Use this field to add the tags groups in the preferred order. For example, if there are three groups on a collection page for Size (Size_Small, Size_Medium, Size_Large), Color (Color_Red), Price range (Price range_1.99-9.99), you could rearrange these to put Price range first by adding "Price range" to the Group order field.
Rearrange the tags listed under groups with the Tag order field. Similar to the Group order field, the Tag order field is used to identify a new sequence for the listed tags (as opposed to the default alphabetical order).
Add the tags in the preferred order, using the full tag as it appears in the Products admin. For example, if there are tags for size:
Size_S, Size_M, Size_L, Size_XL
These would appear in alphabetical order (L, M, S, XL). To change these to order for ascending size, add these to the Tag order field in the preferred order.