A platform officer is a banker who advises the public with the bank's accounts and services, and helps arrange them. The term dates back to at least the early 20th century.
AllBusiness.com's Business Glossary says:
The term platform originated in the period when banking officers sat at desks on a platform slightly elevated above the main banking floor, but today is used to describe the customer service area in a bank's lobby.
These officers are also known as platform officers, or as in your bank, platforms for short.
Here's a job ad from The Miami News, Feb 13, 1971 showing it's a front-of-house customer-services job:
BANK PLATFORM OFFICER
A local national bank has immediate need for experienced general banker. To qualify for this position applicants should nave of 5 years experience and be adept at meeting and dealing with public.
From the Sarasota Herald-Tribune, Jan 23, 1969:
Patricia Davis has been promoted to assistant cashier and will serve as a platform officer.
The following are Google Books snippets and the years may be wrong but they look plausible.
Banking: Journal of the American Bankers Association, Volume 50, Part 2, 1958
PLATFORM OFFICER SERVICE — Opens new account. Advises as to, and arranges for any service.
The Bankers Magazine - Volume 128 - Page viii, 1934:
... bank employee who wonders if he will ever get to be a platform officer, his struggles towards that end notwithstanding.
Trust Companies - Volume 67 - Page 25, 1938:
... for direct mail, or armed with letters of introduction from the "front platform" officer who "contacts" the big loan applicant.
Proceedings of the Common Council of the City of St. Paul - Page 533, 1917:
... Expense to be charged to Health Fund Public Paths Account Salary Account: 1 Platform officer at $900.00 per year, ...
Annual Report - Page 29, Saint Paul (Minn.). Bureau of Health, Saint Paul (Minn.). Dept. of Health, Saint Paul (Minn.). Commissioner of Health - 1915:
Watchmen and policemen 1,702.00
Concrete inspector 15.00
General superintendent of pavilion 455.00
Three cashiers 312.17
Platform officer 257.50 ...