Oruanui eruption
Your probably looking at something the size of this eruption in NZ. VEI of 8, but thats two orders of magnitude over its last eruption.
Any evacuation will have to be from the seaboard ports on the Atlantic. Spain, Portugal, France, Britain and perhaps Norway.
Any evacuation will have to be to someplace with the infrastructure to support the influx of refugees.
that leave the USA, the Portuguese and Spanish colonies which are the closest and the British colonies in BNA.
Beyond that this will upset the entire economic dynamic between the colonial states effected and the colonies supplying the raw resources and cash crops, Brazil and the Spanish colonies will undoergoe a fundamental restructuring of their economies,
Australia is too far away and under developed outside of Sydney ditto the Pampas of Argentina Though I suppose you could see an influx into Buenos Aires and with support from Asuncion and Cordoba perhaps a limited expansion
The USA probably stands to be the primary beneficiary of any such exodus...its close and its open to immigration beyond the Appalachians, but it will bring relations with the natives to a head rather quickly.
BNA is already in the process of clearing land for over a decade already for settlement. the 1790's saw large numbers immigrate to UC largely from the US Now they will come in even larger numbers directly from the UK...not just to UC but to LC and the Maritimes as well. Others will deposit in the cities and towns of the Caribbean Islands which as stated will have to make a transition from traditional plantation agriculture cash crops to more general mixed farming to support the growing towns.
Some plantations will probably survive but others will probably be broken up or be inhabited by large numbers of tenant farmers...
Slave labour under such conditions is not necessary and could see widespread abolition as the economy transitions to a more mixed agricultural base supporting growing towns.
France is particularly badly place...While the Dutch who can afford passage can probably get to the Cape or Guyana ( Of which the Dutch control the bulk at this point) they have few colonies to go to...those that go to the French islands will augment the urban population or become tenants on plantations transitioning from Cash crop production, but the climate is not favourable, yellow fever is endemic in places. but perhaps they can take advantage of the Bourbon family compact and find refuge in the lands of Spain that were turned over to them in 1761... Louisiana and New Orleans for instance nominally in the name of Spain but say under a French Duke perhaps...Louis or Charles.
The French may be in the midst of revolution but the worst excesses haven't occurred yet and the natural disaster may be just the thing to bolster the monarchy.
So you get a two pronged evacuation from France's atlantic ports... republicans to the USA and royalists to the Fr. Caribbean islands and Spanish lands in the Mississippi and perhaps in the sparsely settled Plate Whether the French treasury can afgford to purchase the terr. is a matter of conjecture, probably not. Probably settlement under Spanish auspices but under a French Bourbon Duke as governor.
the Spanish themselves will go to the largely established towns of Central Mexico, the Altiplano, Venezuela and the large islands of the antilles and Northern Florida.
As for the rest the Italians will probably inundate Spain and Portugal first in an attempt to flee makeing mainland Spain largely ungovernable as food supplies begin to dwindle..
The Spanish monarchy probably re-locates to MC in this case but maintains a full claim on Spainitself, same with Portugal.
Just to clarify, it is XVIII C. not XVII.