Correct way to Integrate JAX-RS with CDI?

I used to integrate Service and DAO beans in Jersey REST resources by annotating them with @Path following Java EE tutorial

In general, for JAX-RS to work with enterprise beans, you need to annotate the class of a bean with @Path to convert it to a root resource class. You can use the @Path annotation with stateless session beans and singleton POJO beans.

So my code used to be something like this:

@Path("/")
public class ServiceResource {
   @Inject
   private AccountService accountService;

   @GET
   @Path("/account/get")
   public Account getAccount(@QueryParam("id") String id) {
     return accountService.get(id);
   }
}

@javax.inject.Singleton
@Path("")
public class AccountService {
   public Account get(String id){...}
}

Now, I started integrating a Quartz Job into my application, and I wanted to find a way to inject my AccountService inside a job like this

public class AccountJob implements Job {
  @Inject
  private AccountService accountService;

  @Override
  public void execute(JobExecutionContext jec) throws JobExecutionException {
    accountService.updateAllAccounts();
  }
}

I found this answer that tells to use DeltaSpike to do the Job, so I added the following dependencies to my pom.xml, and without adding any more lines of code to any class the inejection of accountService to my Job works fine

<dependency>
    <groupId>org.apache.deltaspike.modules</groupId>
    <artifactId>deltaspike-scheduler-module-api</artifactId>
    <version>1.7.2</version>
    <scope>compile</scope>
</dependency>
<dependency>
    <groupId>org.apache.deltaspike.modules</groupId>
    <artifactId>deltaspike-scheduler-module-impl</artifactId>
    <version>1.7.2</version>
    <scope>runtime</scope>
</dependency>
<dependency>
    <groupId>org.apache.deltaspike.cdictrl</groupId>
    <artifactId>deltaspike-cdictrl-api</artifactId>
    <version>1.7.2</version>
    <scope>compile</scope>
</dependency>
<dependency>
    <groupId>org.apache.deltaspike.cdictrl</groupId>
    <artifactId>deltaspike-cdictrl-weld</artifactId>
    <version>1.7.2</version>
    <scope>runtime</scope>
</dependency>

However, I realized that when I remove the @Path("") from AccountService, its instance is still injected fine inside ServiceResource, so my questions are the following:

1. Why adding DeltaSpike dependencies made it possible to inject my beans without using @Path on them?
2. By searching more, I understood that DeltaSpike internally uses Weld to do the injection, and since I am already using GlassFish 4.0, I know that Weld is already there, so why the injection is not working by default in my Job class and in ServiceResource class without adding @Path on my beans? Actually why adding @Path is even suggested in the Java tutorial?
3. Is there any bad side effects that I don't see in my code, because I think that I am mixing multiple DI methods here without really understanding how do they work?

Update: After more search, I realize that Jersey doesn't use Weld for dependency injection, instead it uses HK2, a different framework that also happens to be a part of GlassFish, when I try to inject AccountService without using @Path it shows the following exception

org.glassfish.hk2.api.UnsatisfiedDependencyException: There was no object available for injection at SystemInjecteeImpl(requiredType=AccountService,parent=ServiceResource,qualifiers={}...

So this updates the questions to the following:

1. How to make HK2 injections works? // Without using @Path as mentioned in the Java EE Tutorial
2. If I managed to to do DI with HK2, will it be safe to use DeltaSpike to do DI for the Quartz Job? Is it okay to mix two CDI framewroks together to scan the classes and do the injection?

I put my my source code on pastebin; pom.xml is here and the Java is here