Update 23 February 2021 see Gilles Cuniberti here on a related issue of the application of the lex causae to interim proceedings, with the French Supreme Court reversing decades of case-law to hold that interim measures are included in the lex causae, not subject to lex fori.
I am busy on many fronts and not complaining, yet I am sorry if some posts are therefore a little later than planned. A quick flag of Duffy v Centraal Beheer Achmea  EWHC 3341 (QB) in which Coe J noted parties agreed that interim payments are included in the Rome II exemption of evidence and procedure: at 8:
The claim is brought in the English Court against a Dutch motor insurer and it is agreed that the law of the Netherlands applies to this claim in tort. The claimant, as a result of Dutch law has a direct right of action against the insurer and, following the decision in FBTO v Odenbreit  C 463-06, the jurisdiction of the English Court is not an issue. The law of the Netherlands applies (pursuant to Article 41(1) of the Rome II Regulation on applicable law in tort (Regulation 864/2007)). Dutch law will govern limitation, breach of duty and causation as well as the existence of, the nature of and the assessment of damages to which the claimant might be entitled. Matters of procedure and evidence are nonetheless reserved to the forum court (see Article 15 (c) of the Rome II Regulation and Article 1(3)). This is an application for an interim payment which is a procedural application and thus governed by English law. However, when it comes to any assessment of the damages to which the claimant might be entitled on which to base the interim payment decision, Dutch law has to be applied.
Coe J has little reason to disagree however I imagine she would have entertained the issues more had the distinction between Dutch and English law on the interim payment issue been materially different, hence had counsel made diverging noise. For as I have signalled before, the extent of the evidence and procedure exemption is not clear at all.
EU Private International Law. 3rd ed. 2021, Chapter 4, Heading 4.8.