Due to Infusionsoft API restricted, contact information on the site is generally cached.
However, cached contact information is automatically updated during certain events known to iMember360, such as when a tag is assigned from within iMember360 or when an an Infusionsoft HTTP POST is received for a contact.
Outside the immediate area of control of iMember360, iMember360 doesn't know about changes to a contact.
A regular intervals, however, using a setting that you can define in "Plugin Options", iMember360 can automatically refresh the contact cache.
If you often do contact record updates through other API-based applications or Campaign Builder sequences, you can use iMember360's i4w_sync_user module, either as an HTTP POST out of campaign or through the webhooks available in Infusionsoft.