There are two types of JSA. If a claimant has an up-to-date record of National Insurance contributions then (subject, of course, to meeting the relevant requirements, such as actively seeking work) he/she will receive contribution-based JSA, which is NOT means-tested, for up to 6 months. So it would be irrelevant as to whether he/she had any ISAs.
Anyone who is ineligible for contribution-based JSA (such as people with no recent NI contributions or those who've reached the end of the 6-month period) can apply for income-based JSA but that IS means-tested, with ISAs counting as 'savings'.
ISAs also count when assessing entitlement to any other means-tested benefits. This link shows which benefits are, or are not, means-tested:
https://www.moneyadviceservice.org.uk/en/articles/disability-and-sickness-benefits-check-your-entitlements