There is problem with Just Type after updating to 3.0.5. Using Just Type from the home page on your TP uses your default search engine as expected. However, using Just Type when you are already on the web does not use your default search engine. Instead, it will use what you have selected under the Search Using section of Just Type (go to Settings, tap on the Just Type Icon and look under Search Using to see what you have turned on).
This means that if you have a SSL search engine set-up as your default search engine, Just Type will not use that anymore when you are on the web. It also means you may get something really weird for searches if you don't go into Search Using and uncheck anything you don't want. (For example, my seaches started using Wikipedia by default until I unchecked that under the Search Using section of Just Type.)