What an interesting question!
First, check your company policy and your employment requirements regarding use of personal devices for company use. If you are required to download apps, supply and use your personal phone, and use technology as instructed, you're out of luck there. If it's in the requirements, you have agreed to meet those requirements by taking that job on. Now, you say you didn't sign anything in regards to policies. Double check your company policies to be 100% sure that there isn't some sneaky thing hiding somewhere! Some companies get around supplying employees with company devices by saying, "Employee is expected to use technology as required". It is a vague statement, but can arguably mean anything from the work photocopier to your own personal phone. As a rule though, if your company expects you to be downloading apps and using your personal phone for work, there would be a policy for it.
Second, if no policies exist on using personal phones for work, then your company does not have a leg to stand on when it comes to telling you that you must download and use an app that takes up data on your personal phone. If there is no policy on this, ask management where it is in writing that you are expected to have clients call your personal cell phone and download and use an app using your personal data. If management cannot show you, then you have every right to refuse to download it because your personal phone is yours, and you should not have to buy into a data plan, and possibly a new device, for work when they have no policy or previous requirement to do so.
It is your decision now. Do you upgrade your phone, bring sanitizer wipes to wipe it with, continue to have clients call you 24/7, and use a data plan all at your personal cost? Or, do you find a job doing something else?
All that aside, I think using personal devices to store client information is a mistake. I think that client privacy and confidentiality is at risk by having the Crescendo Connect app on your personal phone. What happens to client information if your personal phone is lost, stolen, or hacked? While these issues still exist with a company device, company devices usually have systems and apps in place such as theft-prevention, firewalls to deter hackers (or something to that effect), and GPS tracking.