If you have something like an old windows phone that doesn’t have a working tumblr app — like I do — you are not out of business. You could send your tumblr post via email (btw. that works with many blog systems like WordPress.com etc.)
Go to you options page (symbolized by the cogwheel). There you find the email address you need to post.
Write an Email, in the subject line you have the headline of your post, the email text gets published as the body text of the blog post. If you want to publish pictures, the subject line becomes the text below the picture.
You even can include tags in your posts, just write Hashtags (#yourtag) below the blog text.
What you are not allowed to do: send the email to more than one adress or as cc. Simply concentrate on the standard email and you shouldn’t have any problems.
And why does your Tumblr-Blog not get spammed via this email adress? The email adress is totally randomized, also there is a spam filter behind it. But if you loose your phone, you should definitely change the email adress provided!