It means sticking to terms and conditions - such as the funds not being available for withdrawal until you are 65 or have been in KiwiSaver for five years - that are similar to those for KiwiSaver.
It sounds as if your new employer has a "complying fund" under the KiwiSaver rules.
I asked Michael Raynes, head of marketing and communications at Fisher Funds, to take a look at your questions.
This is what he had to say:
"If you change jobs and are already a member of a KiwiSaver scheme then you will be required to keep making contributions to KiwiSaver.
"If you have been a member of a KiwiSaver scheme for more than 12 months then you do have the option of taking a contributions holiday of between three months and five years.
"All you need to do is complete a simple form or give Inland Revenue a call on 0800 KIWISAVER (549 472).
"Inland Revenue will contact you near the end of your contributions holiday and you can "roll over" your holiday as many times as you like.
"This may be an option for you to consider.
"It's also worthwhile noting that while you are on a contributions holiday there is nothing stopping you from making contributions directly to your provider in order to access your annual member tax credit entitlement from the Government of up to $521.43.
"Opting out of KiwiSaver is only an option for people who are automatically enrolled via the default joining method when they start a new job.
"They can opt out anywhere between two weeks and eight weeks after starting their job.
"It sounds like your employer is exempt from the automatic enrolment rules, however automatic enrolment doesn't apply to you anyway as you are already a member of a KiwiSaver scheme," says Raynes.
To be clear, the automatic enrolment applies only if you're starting a new job and have never been a KiwiSaver member.
When existing KiwiSaver members switch jobs they need to give their new boss a KiwiSaver deduction form (KS2) to let them know if they want to contribute 3 per cent, 4 per cent or 8 per cent of their pay.
If you don't fill in a form your new employer will automatically start deducting 3 per cent from your wages for KiwiSaver.
As Raynes mentions, a KiwiSaver contributions holiday form can halt all contributions from you and your employer.
You can request a contributions holiday to stop contributions to KiwiSaver and join your employer's complying fund if you wish but you cannot opt out.
Disclaimer: Information provided is stated accurately to the best of the respondent's knowledge at the time of publication. It is general in nature and should not be construed, or relied on, as a recommendation to invest in a particular financial product or class of financial product. Readers should seek independent financial advice specific to their situation before making an investment decision.
To have your KiwiSaver questions answered by the NZ Herald's panel of industry players email Helen Twose, helentwose@gmail.com. Sorry, but Helen cannot answer all questions, correspond directly with readers, or give financial advice.