Update 25 02 2022 see further analysis by Matthias Lehmann here.
I cross-referred to the pending preliminary review in C-708/20 Betty Tattersall aka Seguros Catalana Occidente in my review of Flowers v Centro Medico. The CJEU held this morning in Betty Tattersall (which also means the Flowers case may now continue). I call the issue ‘vis attractiva securalia’ which is a term I made up but hopefully usefully summarises the issue. Domicile of the claimant, as readers of the blog will know, is generally of no consequence in EU jurisdictional rules. There are a few exceptions, in particular for the protected category of consumers (for employees, it is the place of habitual performance of the employment contract which is relevant, which often co-incides with their domicile), and for insurance contracts – but in the latter case, it turns out, not of benefit for the injured party.
Ms Tattersall argues that , in relation to EB, who is domiciled at Ireland and owns the holiday home which Ms Tattersall rented and in which she suffered a fall, that a claimant may bring an action against an insurer domiciled abroad under A13(3) BIa. A13 effectively piggy-backs claims of the injured party viz liability insurance, unto the by virtue of A11-12 extended forum possibilities for the insured, the policyholder or beneficiary of the insurance policy. In her view, the existence of a ‘dispute’ between the insurer and the insured regarding the validity or effect of the insurance policy is not necessary in that regard. The only requirement under A13(3), she suggests, is that such an action against the insured is provided for by the law governing direct actions against the insurer, in this case Spanish law. EB by contrast argues that Ms Tattersall’s claim is not an insurance claim and cannot become one merely because it was brought in the same action as the direct action against the insurer.
One can see why Ms Tattersall attempted to join EB into the English procedural bath: the insurer is an interesting defendant of course for it has deeper pockets; however EB’s insurer argue that the limitations and restrictions in the insurance policy meant that the policy did not extend to EB’s use of the property for the purpose of accommodating third parties on holiday against payment. Should that argument hold on the merits, Ms Tattersall’s claim will fall flat and she would have to sue EB separately, in Ireland.
The CJEU insists on the need to read the insurance Section with its specific purpose in mind: the protective effect intended by the Section is aimed at those considered to be in a weaker position vis á vis the insurer: the insured and the injured person are considered to be the weaker party in the contractual relationship, not the third party who is in a non-contractual relationship to both. Therefore 
to justify the application of the special rules of jurisdiction laid down in Section 3 of that regulation, the action before the court must necessarily raise a question relating to rights and obligations arising out of an insurance relationship between the parties to that action.
The Court does [35-36] acknowledge recital 16 BIa which refers to the objective of facilitating the proper administration of justice. It concedes that the involvement, by the injured person, of the insured, as a third party to the proceedings before the court seised, would make it possible to avoid the risk of the coexistence of two parallel sets of proceedings. Nevertheless, the emphasis must fall on the effet utile of A7(2): allowing the injured person to bring an action against the insured on the basis of A13(3) would amount to circumventing the forum delicti rules of A7(2). Each injured person could then bring an action against the insurer on the basis of A13(2), to benefit from the more favourable provisions of A10 to 12 in order, subsequently, to bring an action against the insured, as a third party to those proceedings, on the basis of A13(3).
The CJEU’s’ formal reply therefore is that
Article 13(3) of Regulation (EU) No 1215/2012 of the European Parliament and of the Council of 12 December 2012 on jurisdiction and the recognition and enforcement of judgments in civil and commercial matters must be interpreted as meaning that, in the event of a direct action brought by the injured person against an insurer in accordance with Article 13(2) thereof, the court of the Member State in which that person is domiciled cannot also assume jurisdiction, on the basis of Article 13(3) thereof, to rule on a claim for compensation brought at the same time by that person against the policyholder or the insured who is domiciled in another Member State and who has not been challenged by the insurer.
Readers may enjoy the strategic off the cuff claim engineering possibilities which I entertained with Sarah Crowter QC.