If Steam Input is causing problems, can you please open the Controller configuration within Steam, and tell us what configuration profile you are using? Is it the Official one, or have you made personal changes?
Sadly I still cannot repro this problem on my computer. Please note that with Purzzle's advice above, this may help if your Warframe controller config is still default, but it also might not do anything since you can set Deadzones in your Warframe-specific controller setup:
1) Bring up Steam overlay
2) Click the "Controller Settings" icon
3) Click on "Edit Layout"
4) In the config editor, click on the "Joysticks" entry
5) Under Joystick Behavior, click the small [Gear] icon
6) Under Joystick Settings, scroll down a bit to find Deadzones\Deadzone Source
I'd be curious how many of you are using "None", "Controller Preference", and "Custom"
To remedy this issue, please completely close and then restart your Steam client to get the latest update which addresses various deadzone issues:
https://store.steampowered.com/news/app/593110/view/6216734321427106459
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